math.GT daily digest: 33 submissions for 14 October 2026

New submissions

A Counterexample to Three Conjectures of Luo

• Authors: Qilong Guo
• arXiv: 2610.13979
• Comments: 5 pages, 1 figure
• Subjects: Geometric Topology (math.GT)

We give a single counterexample to Conjectures 1--3 as stated in Luo's paper: a minimal two-tetrahedron triangulation of the lens space L(3,1) with a null-homotopic loop edge. The proof uses quadrilateral matching equations, an explicit calculation of shape parameters, and known results on volume maximization.

Tight surgeries on torus knots

• Authors: John B. Etnyre, Hyunki Min, Bülent Tosun, Konstantinos Varvarezos
• arXiv: 2610.14218
• Comments: 82 pages, 22 figures
• Subjects: Geometric Topology (math.GT); Symplectic Geometry (math.SG)

We give a complete classification of tight contact structures on manifolds obtained from any surgery along any torus knot, which provides the first such classification on an infinite family of knots. The main tools are the classification of non-loose torus knots, bordered contact invariants via their immersed curve interpretations, and non-thickenable tori in knot complements. As a byproduct of this classification, we also give the first classification of contact structures on some surface bundles over the circle with fibers of genus larger than $1$. The symplectic fillability of these contact structures is also studied and leads to, among other things, the disproof of a conjecture of Ghiggini and Van Horn-Morris on Stein fillability of some contact structures on a Brieskorn sphere.

Shake concordance in the topological concordance class of the Hopf link

• Authors: Weizhe Shen
• arXiv: 2610.14575
• Comments: 16 pages, 3 figures
• Subjects: Geometric Topology (math.GT)

Within the topological concordance class of the Hopf link, we construct infinitely many classes under the equivalence relation generated by smooth $0$-shake concordance. Each contains infinitely many smooth concordance classes represented by links that are pairwise strongly $0$-shake concordant and whose second components have unbounded smooth slice genus.

Boundary of Anosov coaffine representations

• Authors: Marit Bobb, James Farre
• arXiv: 2610.14897
• Comments: 80 pages, 8 figures
• Subjects: Geometric Topology (math.GT)

Let be a torsion-free hyperbolic group dividing a properly and strictly convex domain , and let be the inclusion. We study representations of $\Gamma$ into the coaffine group that are deformations of and that lie on the boundary of the locus of projective Anosov representations. In this setting, we identify a canonical limit set $\Lambda$ for the action and study its fine geometric features which are, in a suitable sense, stable. We prove the existence of an ending lamination that encodes the failure of the Anosov condition and the non-existence of a Cannon--Thurston map. Under certain conditions, we compute the Hausdorff dimension and show that the corresponding measure is positive.

One boundary, infinitely geometries

• Authors: Jiming Ma
• arXiv: 2610.15406
• Subjects: Geometric Topology (math.GT)

Let $N$ be a 3-dimensional integral homology sphere. We prove the existence of a sequence of 4-dimensional topologically negatively curved manifolds , , satisfying the following:

(1) all aspherical manifolds have the same universal cover depending only on $N$;

(2) all fundamental groups are hyperbolic and share the same Gromov boundary depending only on $N$;

(3) the groups represent infinitely many distinct quasi-isometry classes.

The last conclusion, which represents the new feature, shows that negatively curved geometries in dimension 4 exhibit substantially richer structure than those in dimension 3.

Symplectic four-manifolds and hyperbolic $\pi$-orbifolds

• Authors: Francesco Lin, Bruno Martelli
• arXiv: 2610.15698
• Comments: 28 pages, 9 figures
• Subjects: Geometric Topology (math.GT); Symplectic Geometry (math.SG)

We construct closed symplectic 4-manifolds admitting the structure of hyperbolic $\pi$-orbifold, addressing LeBrun's conjecture. Our simplest example has Euler characteristic $304$, is tessellated by $64$ copies of the right-angled hyperbolic $120$-cell and admits a four-fold branched covering over a product of two surfaces of genus $4$.

The inf spectrum of moduli space

• Authors: Ara Basmajian, Sayantika Mondal, Hugo Parlier
• arXiv: 2610.15926
• Comments: 26 pages
• Subjects: Geometric Topology (math.GT); Algebraic Geometry (math.AG)

Given a surface of genus , its inf spectrum is the ordered multiset of inf lengths of curves on the surface, the infimum being over all hyperbolic metrics. We show that the inf spectrum has exponential growth with coefficients that only depend on g, improving the earlier double exponential upper bound. The proof involves developing a number of tools including the process of "thickening" a surface and the notion of model surfaces. These tools may be of independent interest.

On infinite knot families with the same HOMFLYPT polynomial

• Authors: Yuki Matsushima
• arXiv: 2610.16017
• Comments: 19 pages, 28 figures
• Subjects: Geometric Topology (math.GT)

In this paper, we focus on the examples constructed by Kanenobu and provide new family knots with the same HOMFLYPT polynomial invariants, which are distinguished by the Kauffman polynomial.

Loop Fundamental Quandles: A Geometric Generalization of the Knot Quandle

• Authors: Seiichi Kamada
• arXiv: 2610.16056
• Subjects: Geometric Topology (math.GT)

The knot quandle, introduced independently by Joyce and Matveev, admits a geometric description in terms of nooses. Motivated by this description, we introduce the \textit{loop fundamental quandle} of a pair $(X,A)$ with a fixed base point . Its elements are represented by pairs consisting of a loop in $A$ and a path joining the base point of the loop to the fixed base point $\ast$. More generally, for a loop condition $P$ on $A$, invariant under free homotopy, we define the loop fundamental quandle .

We establish functoriality and homotopy invariance of the loop fundamental quandle and show that it admits a natural augmented quandle structure over . For a knot $K$ in , applying the construction to its exterior gives the \textit{knot loop quandle} . Appropriate choices of the loop condition recover the knot quandle, its $n$-th power quandles, and the full knot quandle. The construction is inspired by Joyce's noose-theoretic approach, but allows loop data that need not arise as the boundary of a disk satisfying the noose condition.

Lens spaces that cannot be obtained by two integral surgeries

• Authors: Marco Golla, Marc Kegel
• arXiv: 2610.16431
• Comments: 18 pages
• Subjects: Geometric Topology (math.GT)

In this article, we demonstrate that there exists an infinite family of lens spaces L(p,q) that cannot be obtained from the 3-sphere by two integral surgeries. The first such lens space in our family is L(177,29).

An Algebraic Matching Algorithm for the Genus of Grid Diagrams

• Authors: Jun Wang, Shasha Yang
• arXiv: 2610.16514
• Subjects: Geometric Topology (math.GT)

Grid diagrams encode knots and links combinatorially through an (n,n) winding matrix W(G). A fundamental invariant of the grid diagram is its genus g(G), which records essential topological information about the underlying knot. We give an algebraic algorithm that computes g(G) directly from W(G). The method repurposes the Hungarian algorithm ,after a column normalization that makes the matrix non-negative, it applies row-column reductions and minimum-vertex-cover corrections until the zero entries admit a perfect matching, equivalently until the minimum marking number equals n. By Konig's theorem the resulting permutation defines a distinguished grid state, and g(G) is then read from this matrix via the classical grid homology formula (Ozsvath-Stipsicz-Szabo). The novelty of this paper is the algorithm and its strongly polynomial analysis; the underlying invariant is known grid-homology theory. We illustrate the method on the trefoil and additional examples, and discuss extensions to (m,n) matrices and grid-move navigation toward the knot genus g(K).

Knot Floer homology of fibered positive links

• Authors: Zhechi Cheng
• arXiv: 2610.16539
• Comments: 23 pages, 7 figures
• Subjects: Geometric Topology (math.GT)

We determine the Maslov-graded next-to-top term of knot Floer homology for fibered positive links. Its rank in Maslov grading (-1) is the number of nontrivial prime connected-sum factors plus the number of components minus one, and the remaining summand is supported in Maslov grading zero. For a knot, the dimension of this remaining summand is determined by its Alexander polynomial. The proof combines a preferred-crossing construction with reductions of generalized Seifert surfaces to planar pretzel surfaces and a graded skein induction. We also obtain bounds on the fixed points of monodromies for fibered positive knots.

The symmetry group of Turk's head knots

• Authors: Werner Stanggassinger
• arXiv: 2610.16600
• Comments: 17 pages
• Subjects: Geometric Topology (math.GT)

For p, q >= 3 with gcd(p,q) = 1 we show that the symmetry group of the Turk's head knot Th(p,q), the closure of the braid (sigma_1 sigma_2^{-1} sigma_3 sigma_4^{-1} ... sigma_{p-1}^{+-1})^q, is the dihedral group of order 4q. This proves Conjecture R of Di Prisa and Şavk for q >= 3; the case p = 3 is due to Sakuma and Weeks. The argument is diagrammatic: by the flyping theorem of Menasco and Thistlethwaite, the symmetries of a knot with a prime, reduced alternating diagram without non-trivial flypes are the symmetries of the diagram (we write out a proof for the diagrams at hand), and we show that the standard diagram of Th(p,q) has no non-trivial flypes and exactly 4q symmetries. The chirality of Th(p,q) for even p, which also follows from a theorem of Murasugi, is visible in the group. We compare the argument with the geometric one of Sakuma and Weeks for p = 3.

Homotopy Self-Equivalences of and a Braid for non-orientable $4$-Manifolds

• Authors: Mehmetcik Pamuk
• arXiv: 2610.16606
• Comments: 25 pages
• Subjects: Geometric Topology (math.GT); Algebraic Topology (math.AT)

We compute the group of based homotopy classes of self-homotopy equivalences of the non-orientable $4$-manifold \RP^2\times S^2!. It is an elementary abelian $2$-group of rank $5$. The subgroup of classes whose based lift to the universal cover has degree $+1$ has rank $4$ and is isomorphic to the group of free homotopy classes. The group maps onto the group of self-equivalences of the algebraic $2$-type, which has order $8$, with kernel \pi_4(\RP^2\times S^2)\cong(\Z/2)^2! generated by pinch-fold maps; that these maps are independent is shown by an adjunction argument. We then construct a non-orientable analogue of the Hambleton--Kreck braid of exact sequences in dimension $4$, for non-orientable manifolds with spin universal cover, stated for finite fundamental group. We apply the braid to \RP^2\times S^2! and to \RP^4!, and for the Hambleton--Hillman manifold with fundamental group we determine the normal $1$-type and show that self-equivalences act on through diagonal sign matrices. For \RP^2\times S^2! the pinch-fold maps are detected by twisted spin bordism, and, assuming facts from surgery theory stated as hypotheses, exactly one of the three non-trivial pinch-fold maps is homotopic to a homeomorphism.

On Intersection of Character Varieties Associated to Dehn Fillings of the Whitehead Link and Its Generalization

• Authors: Jiayu Wan, Charles Katerba
• arXiv: 2610.16731
• Subjects: Geometric Topology (math.GT)

The canonical component of the character variety of a hyperbolic 2-bridge link complement M is an algebraic surface, from the work of Thurston. If we fix a boundary component T of M and perform a Dehn-filling on T, we get a 1-cusped manifold whose character variety is commonly a generalized curve that is naturally embedded in the character variety of M. If we perform distinct Dehn-fillings on M, we get various generalized curves on the canonical surface. In this paper, we analyze how these curves intersect with each other in the surface and study the topological implications for these intersection points. We also classify the intersection points that correspond to reducible characters, using the twisted Alexander polynomials associated to the Dehn-fillings. Throughout the paper, we use the Whitehead link as a motivating example to illustrate our core methodology, while some generalizations to other 2-bridge links will also be discussed.

Morita Invariance of Saturated and Split Subgroupoids for Orbifold Embeddings

• Authors: Zhenxi Huang, Keyin Chen
• arXiv: 2610.16885
• Comments: 36 pages
• Subjects: Geometric Topology (math.GT)

Borzellino and Brunsden introduced a general notion of suborbifold and proved that a suborbifold is the image of a complete orbifold embedding if and only if it is both saturated and split. Their definitions and proofs are formulated in the classical language of orbifold charts. In this paper we translate these notions into the language of proper étale Lie groupoids.We introduce the groupoid analogues of saturation and splitting, which we call \emph{orbit saturation} and \emph{stabilizer splitting}, and prove that they coincide with the chart-based conditions. Our main theorem states that a subgroupoid is the image of a complete orbifold embedding if and only if it is both orbit saturated and stabilizer split. We then prove that these notions are Morita invariant: if two orbifold groupoids are Morita equivalent, then their orbit saturated and stabilizer split subgroupoids correspond naturally to each other. This solves an open problem raised by Mestre and Weilandt and explains why the embedding definition of Cho--Hong--Shin fails to be Morita invariant. Along the way we provide detailed examples, including the diagonal embedding, the non-split example of Borzellino and Brunsden, and explicit Morita equivalences.

Ideal Poisson--Voronoi tessellations for Finsler metrics on symmetric spaces

• Authors: Colin Davalo, J. Maxwell Riestenberg, Anna Wienhard
• arXiv: 2610.17045
• Comments: 72 pages, 20 figures. Comments and suggestions are welcome
• Subjects: Geometric Topology (math.GT); Differential Geometry (math.DG); Probability (math.PR)

Ideal Poisson--Voronoi tessellations are random tessellations that arise as limits of Voronoi diagrams for Poisson point processes as their intensity tends to zero. For the Riemannian metric on a symmetric space of higher rank, Frączyk, Mellick, and Wilkens (arXiv:2307.01194) proved that the corresponding ideal Poisson--Voronoi tessellation is almost surely completely connected, with an unbounded side between any two cells. This contrasts sharply with the geometry of ideal Poisson--Voronoi tessellations in hyperbolic spaces studied by D'Achille, Curien, Enriquez, Lyons, and Ünel (arXiv:2303.16831). In this paper we introduce and study ideal Poisson--Voronoi tessellations for Finsler metrics on higher rank symmetric spaces. We show that ideal Poisson--Voronoi tessellations with respect to polyhedral Finsler metrics can exhibit either behavior seen in these previous works: generically they resemble the hyperbolic case, where almost surely all cells have bounded sides.

We further introduce the ideal Selberg--Poisson--Voronoi tessellation of the space of positive definite symmetric matrices, which has particularly nice properties.

Turaev cobracket, synthetic geometry and applications

• Authors: Moira Chas, Arpan Kabiraj
• arXiv: 2610.17235
• Comments: 20 pages, 9 figures. Comments are welcome
• Subjects: Geometric Topology (math.GT)

A teardrop geodesic on a hyperbolic surface is a closed curve that is geodesic except at exactly one point, called its vertex. One imagines a closed curve with one point held down as it deforms to a geodesic. For each teardrop geodesic, we give an explicit geometric construction of the closed geodesic in its free homotopy class. This construction also yields a relation between the length of the teardrop geodesic, the angle at its vertex, and the length of its geodesic representative. We then apply the construction to a self-intersecting closed geodesic at a chosen self-intersection point. Since, at that point, the geodesic splits into two directed teardrop geodesics, our construction gives a geometric description of Turaev's cobracket in terms of geodesic representatives. Using this description we prove that if two self-intersection points yield a pair of canceling terms in the cobracket, then the angle at these points and the lengths of the small loops determined are the same.

Point Processes and Gap Statistics for Translation Surfaces

• Authors: Kai Fu, Anthony Sanchez
• arXiv: 2610.17277
• Comments: 38 pages
• Subjects: Geometric Topology (math.GT); Dynamical Systems (math.DS); Probability (math.PR)

We study the behavior of saddle connection directions on translation surfaces from the point process viewpoint. We define a direction point process for saddle connections of length at most on every translation surface. Given a general ergodic $\mathrm{SL}(2,\mathbb{R})$-invariant measure $\mu$ on a stratum of translation surfaces, we also define a slope point process associated with $\mu$. By utilizing the dynamics and geometry of strata, we show that for almost every translation surface, the direction point processes, rescaled by , converge in distribution to the slope point process as . Using Palm distribution theory, we prove the existence of limiting joint gap distributions and obtain new regularity results for gap distributions associated with the general $\mu$. Finally, we study how these point processes and joint gap distributions behave as the genus $g$ tends to infinity. In the principal stratum, we show that the slope point processes, rescaled by , converge in distribution to a Poisson point process. By passing to the corresponding Palm distributions, we show that the rescaled slope gaps converge jointly to independent exponential random variables, which is in stark contrast to the known non-exponential gap distributions in a fixed genus.

Purely non-free actions on Riemann surfaces

• Authors: Rubén A. Hidalgo, Jhony S. Leyca
• arXiv: 2610.17405
• Subjects: Geometric Topology (math.GT); Complex Variables (math.CV)

A group of conformal automorphisms of a Riemann surface is said to act purely non-free, or to produce a gpnf-action, if each of its finite-order elements has fixed points.

It is known that every finite group admits a gpnf-action on a suitable closed Riemann surface of genus at least two. If $G$ is an infinite countable group, and $X$ is an infinite-type orientable surface, without planar ends and whose space of ends is self-similar, then we observe that there is a Riemann surface structure on $X$ admitting a gpnf-action by $G$.

We obtain upper bounds for those finite groups producing a gpnf-action on a closed Riemann surface of genus .

If $G$ is a finite group, then its purely non-free genus is the minimum genus of at least two of a closed Riemann surface admitting a gpnf-action by $G$. This parameter is already known for cyclic, abelian non-cyclic groups, \mathcal A}_{4!, \mathcal A}_{5! and \mathfrak S}_{4!. For general $G$, we provide the value of , correcting a previous statement on this value. In particular, we observe that every genus is the purely non-free genus of some group.

As an application, we describe the minimal purely non-free actions for the family of metacyclic groups where and is such that .

$3$-manifold groups are linear

• Authors: Xiaolei Wu, Shengkui Ye
• arXiv: 2610.17608
• Comments: 24 pages
• Subjects: Geometric Topology (math.GT)

We prove that the fundamental group of every compact graph $3$-manifold is linear over the complex numbers. As a corollary, all fundamental groups of compact $3$-manifolds are linear over the complex numbers.

A parity constraint on the topological numbers of self-complementary triply-periodic surfaces

• Authors: Roberto De Leo
• arXiv: 2610.18416
• Comments: 5 pages
• Subjects: Geometric Topology (math.GT); Dynamical Systems (math.DS)

The stability zone of Novikov's problem of planar sections of triply periodic surfaces are labeled by indivisible triples of integers, which we call the soul of the zone. Which triples may occur is not known. We show that, if a Morse function $f$ on admits a translation with , so that the sets and are congruent, then in the generic genus-$3$ situation every topological number $L$ satisfies . The mechanism is that the electron/hole type of a null-homologous closed trajectory is invariant under the period lattice and is reversed by $\tau$. For and the $\mu$-cube, this means that the sum of the components of each soul is odd.

A proof of the framed LMOV conjecture for links

• Authors: Kefeng Liu, Pan Peng, Shengmao Zhu
• arXiv: 2610.18618
• Comments: 40 pages
• Subjects: Geometric Topology (math.GT); Mathematical Physics (math-ph); Quantum Algebra (math.QA)

We prove the Labastida--Mariño--Ooguri--Vafa conjecture for oriented links with arbitrary integer framings. Consequently, the framed reformulated invariants have finite integral LMOV expansions for every integer framing vector.

Stably exotic knotted surfaces up to equivalence

• Authors: Daniel Galvin, Daniel Kasprowski
• arXiv: 2610.18783
• Comments: 3 pages
• Subjects: Geometric Topology (math.GT)

In this short note we show the existence of stably exotic knotted surfaces in 4-manifolds in the sense that the embedded surfaces are topologically equivalent but are not smoothly equivalent even after any number of internal and external stabilisations.

The Links--Gould polynomial of an alternating link is alternating

• Authors: Matthew Harper, Ben-Michael Kohli
• arXiv: 2610.18803
• Comments: 40 pages
• Subjects: Geometric Topology (math.GT)

Building on work of Kauffman--Saleur and earlier work of the second author, we derive a determinant formula for the Links--Gould polynomial of links. As an application, we prove a 20-year-old conjecture of Ishii: for any alternating link, the Links--Gould invariant is an alternating polynomial.

Arithmetic hyperbolic manifolds with bounded rank

• Authors: Matthew Zevenbergen
• arXiv: 2610.18841
• Comments: 12 pages
• Subjects: Geometric Topology (math.GT)

We prove that closed arithmetic hyperbolic $n$-manifolds of bounded rank have bounded adjoint trace field degree, and consequently have lower bounded injectivity radius. From this, we obtain a number of corollaries. In particular, we obtain that closed arithmetic hyperbolic $3$-manifolds of bounded rank are contained in finitely many commensurability classes, and describe these commensurability classes. Additionally, it follows that for closed arithmetic hyperbolic $3$-manifolds, Heegaard genus is equal to rank for all but finitely many manifolds of each rank.

Cross submissions

Localization of Floer homology for -actions

• Authors: Erkao Bao, Tyler Lawson, Cheuk Yu Mak
• arXiv: 2610.14468
• Cross-list: math.SG
• Comments: 50 pages
• Subjects: Symplectic Geometry (math.SG); Differential Geometry (math.DG); Geometric Topology (math.GT)

For an odd prime $p$, we prove a Smith inequality over for exact Lagrangian Floer homology under a symplectic -action, assuming an equivariant stable normal trivialization compatible with the Lagrangians and the required relative Pin data. As an application, we obtain a rank inequality between the symplectic Khovanov homology of a $p$-periodic link and that of its quotient. These results extend the involutive localization of Seidel and Smith.

The main construction is a stabilized chain complex. At every invariant intersection point we adjoin the Morse complex of a finite-dimensional normal spectral sphere, whose generators lie in free -orbits. The differential counts holomorphic strips coupled to sphere half-trajectories by a one-sided weighted asymptotic evaluation. We prove transversality, a uniform spectral cutoff, and the compactification and gluing statements needed for the chain identity. The stabilized complex is quasi-isomorphic to the ordinary Floer complex and contains the complex of the fixed data as a subcomplex with free quotient, so the algebraic Smith inequality applies.

Continuum-many discontinuous actions of on manifolds

• Authors: Segev Gonen Cohen
• arXiv: 2610.15653
• Cross-list: math.DS
• Comments: Comments welcome!
• Subjects: Dynamical Systems (math.DS); Group Theory (math.GR); Geometric Topology (math.GT)

For any , we construct a continuum of non-conjugate actions by homeomorphisms of on the $n$-sphere that do not extend to a continuous action of . We do this by adapting a blow-up construction of Bowden and Mann. We motivate studying these actions and note down some related observations.

A Sharp Lower Bound for Integral Menger Curvature

• Authors: Sebastian Scholtes
• arXiv: 2610.15981
• Cross-list: math.CA
• Subjects: Classical Analysis and ODEs (math.CA); Differential Geometry (math.DG); Geometric Topology (math.GT)

We prove that round circles are the unique minimisers of integral Menger curvature among embedded closed curves $\gamma$ of prescribed length $L$ for every , i.e. , with equality if and only if $\gamma$ parametrises a round circle. The proof combines a three-point symmetrisation, an analysis of diagonal truncations, and the periodic Wirtinger inequality. For , known self-avoidance and regularity results extend the minimisation result to closed rectifiable curves without assuming embeddedness or smoothness, provided the length of the curve image equals $L$.

In particular, detects the unknot and is basic for , thereby answering a question posed repeatedly in the literature.

The triangular metric on projective surfaces

• Authors: León Carvajales, Xian Dai, Beatrice Pozzetti, Anna Wienhard
• arXiv: 2610.16487
• Cross-list: math.DG
• Comments: 51pages, comments welcome
• Subjects: Differential Geometry (math.DG); Geometric Topology (math.GT)

In \cite{ThurstonStretch} Thurston introduced stretch paths and stretch maps between hyperbolic surfaces. In this paper we extend similar constructions to the space of convex real projective structures on surfaces. Using Fock-Goncharov-like parameters, we introduce stretch paths and construct explicit stretch maps between the projective surface. We show that stretch maps are --Lipschitz with respect to a triangular metric we introduce on the projective surface. This allows us to gain control on several length functions on an open set of the space of convex real projective structures (those where there is no ``local back--tracking"). As an application we obtain pointwise upper bounds for the Hilbert entropy of some convex real projective structures in terms of Fock-Goncharov-like parameters.

Essential factors for surface homeomorphisms

• Authors: Alejo García-Sassi, Fábio Tal
• arXiv: 2610.16743
• Cross-list: math.DS
• Comments: 34 pages, 1 figure
• Subjects: Dynamical Systems (math.DS); Geometric Topology (math.GT)

Let $f$ be a homeomorphism of a closed orientable surface of genus at least one that is isotopic to a pseudo-Anosov homeomorphism, possibly relative to a finite invariant set. We construct an intrinsic monotone factor by collapsing the maximal continua whose iterates have uniformly bounded diameter in the universal cover. The quotient is homeomorphic to the original surface and the factor is isotopic to $f$ and has several strongly chaotic dynamical features. It is infinitely continuum-wise expansive, tight, and topologically mixing, and it has a dense family of rotational horseshoes, dense periodic points, and a single topological homoclinic class. The factor can be taken as an area-preserving homeomorphism. The quotient preserves stable translation length on the fine curve graph and the applicable homological rotation sets. When $f$ is , a companion paper gives a unique measure of maximal entropy for the factor; it has full support and is Bernoulli.

Very high genus double Hurwitz numbers via mixing times

• Authors: Baptiste Louf, Lucas Teyssier
• arXiv: 2610.16818
• Cross-list: math.CO
• Comments: 13 pages, 3 figures
• Subjects: Combinatorics (math.CO); Geometric Topology (math.GT); Probability (math.PR)

We obtain very high genus asymptotics for double Hurwitz numbers when both the size $n$ and the genus $g$ go to infinity, under the constraint that $g$ grows much faster than $n$, more precisely that . Our proof relies on adapting arguments about the mixing time of the transposition random walk introduced by Diaconis and Shahshahani.

Cohomology ring of the strata of holomorphic differentials of genus 3

• Authors: Prabhat Devkota, Myeongjae Lee
• arXiv: 2610.17985
• Cross-list: math.AG
• Subjects: Algebraic Geometry (math.AG); Geometric Topology (math.GT)

We prove that the rational Chow ring of every connected component of the multi-scale compactifications of the genus three strata and $\mathcal{H}(3,1)$ is generated by boundary-stratum classes. Our proof shows Chow-Künneth generation property of boundary strata of the multi-scale compactification by reducing the boundary analysis to lower-genus generalized strata of meromorphic differentials, including residueless loci, described through plane-quartic and plane-cubic models. As a consequence, the rational cycle-class map is an isomorphism and the compactifications have no odd rational cohomology.