math.GT daily digest: 8 submissions for 23 October 2026

New submissions

Injectivity and continuity of the intersection form in infinite type

• Authors: Tommaso Cremaschi, Didac Martinez-Granado
• arXiv: 2610.30420
• Subjects: Geometric Topology (math.GT)

We study two fundamental properties of the intersection pairing between geodesic currents on infinite-type surfaces which are classical in the finite-type closed setting: injectivity of the marked length spectrum and continuity of the intersection form. We show that geodesic currents on infinite-type surfaces of the first kind are determined by their intersection numbers with closed curves, extending Otal's marked length spectrum rigidity argument from finite-type to infinite-type surfaces. In contrast, we prove that the intersection pairing is not continuous in general for the natural topologies by constructing explicit counterexamples. We then prove sufficient criteria for continuity of intersection numbers for infinite-type surfaces.

A homological approach to Dax invariants

• Authors: Jae Choon Cha
• arXiv: 2610.30837
• Comments: 15 Pages
• Subjects: Geometric Topology (math.GT)

We present a homological construction of Dax invariants in 4-manifolds that is intrinsic to the topological category and requires neither smoothing nor generic representatives. Applications include an extension of the invariant of Cha-Kim to neat disks without assuming local flatness, and a topological definition of the Dax map for arc spaces that yields a short alternative proof of the topological Dax isomorphism theorem.

Triangulation of orbifolds with corners

• Authors: Hao Yu
• arXiv: 2610.31001
• Subjects: Geometric Topology (math.GT); Algebraic Topology (math.AT)

We prove that every compact orbifold with corners admits a triangulation in which the image of every codimension one face is a subcomplex. Faces need not be embedded, and the local groups may permute boundary components. The proof turns the boundary hyperplanes of linear charts into mirrors by means of the squaring map, which, unlike the folding , is compatible with smooth changes of charts, and then applies the triangulation theorem for orbit spaces of proper Lie groupoids.

Euler characteristic and flat cohomology of convex projective $4$-manifolds

• Authors: Andrea Tamburelli
• arXiv: 2610.31085
• Comments: 19 pages
• Subjects: Geometric Topology (math.GT)

Let be a closed properly convex real projective $4$-manifold. We prove the Chern-Hopf-Thurston conjecture for this class of manifolds, i.e. . The argument transfers Akagawa's double-form identity on the Cheng--Yau cone over $\Omega$ to a Bochner identity on $M$, from which we deduce that whenever $q whenever $q<p(n+1-p)/(n+1)$, in arbitrary dimension $n$, for some flat bundle $E$ naturally attached to $M$. In dimension four, this implies that the cohomology with coefficients in $\Lambda^2E^*$ concentrates in degree two.

On the Concordance Invariants of Cable Links

• Authors: Aadhishwaran Bhuvaraghamoorthy
• arXiv: 2610.31654
• Comments: 22 pages, 2 figures
• Subjects: Geometric Topology (math.GT)

We study the Beliakova--Wehrli link $s$-invariant and Cavallo's link $\tau$-invariant of coherently oriented cables. For knots satisfying extremal four-ball genus and maximal self-linking hypotheses, we establish bounds for the $s$-invariant of $(p,q)$-cables, where $p$ and $q$ are not necessarily coprime, and show that these bounds are sharp under certain conditions. For the $\tau$-invariant, we prove analogous bounds for arbitrary companion knots and exact formulas whenever . Specializing to the coherently oriented cable links associated to an $n$-framed knot, we apply these bounds to the lasagna $s$-invariant of Ren and Willis. The resulting applications provide upper bounds for the lasagna $s$-invariant of knot traces and a criterion for distinguishing homeomorphic zero traces up to orientation-preserving diffeomorphism.

Cross submissions

Alexander Torsion and Floer Comparisons in the BV-BFV Formalism

• Authors: Nima Moshayedi
• arXiv: 2610.30192
• Cross-list: math-ph
• Comments: 34 pages
• Subjects: Mathematical Physics (math-ph); High Energy Physics - Theory (hep-th); Geometric Topology (math.GT); Quantum Algebra (math.QA)

We compare relative Abelian BF torsion with the Alexander-graded Euler characteristic of knot Floer homology. A meridional annulus boundary condition identifies the normalized relative torsion with the Alexander polynomial. One exact prime-cyclotomic torsion value recovers all its coefficients under a sharp genus bound, compatibly with connected-sum gluing and branched-cover formulas. We compute interface contractions and obstructions to scalar comparisons, including the pairing defect of two-sector reduction for the degree-zero torus algebra. A six-generator dg resolution yields an equivalence of perfect-module categories preserving derived pairings and admits a classical one-dimensional BV-BFV realization. In the fixed nonresonant polynomial quantum BFV sector, over characteristic zero with $\hslash$ inverted, both states and Weyl observables reduce to a vacuum field; a Hochschild invariant obstructs a Morita equivalence with the degree-zero torus algebra. These results do not establish a full geometric BV-BFV/Floer equivalence.

Quantum field theory and four-manifolds: Perspectives from physics and geometry

• Authors: Niklas Garner, Martijn Kool, Jan Manschot, Yuuji Tanaka
• arXiv: 2610.30288
• Cross-list: hep-th
• Comments: 138 pages
• Subjects: High Energy Physics - Theory (hep-th); Algebraic Geometry (math.AG); Differential Geometry (math.DG); Geometric Topology (math.GT); Quantum Algebra (math.QA)

These lecture notes are based on lecture series by the authors for the Summer School 2025 on ``Physical mathematics of quantum field theory" at the University of Massachusetts Amherst organized by Owen Gwilliam, Chris Elliott, and Matteo Lotito. The lectures centred around algebraic structures arising from twists of supersymmetric quantum field theories, correlation functions of topologically twisted supersymmetric gauge theories, and their mathematical counterparts as intersection-theoretic invariants associated to moduli spaces of instantons, semistable sheaves, or Higgs sheaves on four-manifolds or complex projective surfaces.

Conway's thrackle conjecture: a new upper bound of

• Authors: Dániel Gábor Simon
• arXiv: 2610.31589
• Cross-list: math.CO
• Comments: 7 pages, 2 figures
• Subjects: Combinatorics (math.CO); General Topology (math.GN); Geometric Topology (math.GT)

A thrackle is a drawing of a graph in the plane in which every pair of edges meets exactly once, either at a common endpoint or at a proper crossing. Conway conjectured that every thrackle has at most as many edges as vertices. We prove that every thrackle on vertices has at most edges. The proof combines Pammer's computer-assisted verification of the conjecture for graphs on at most twelve vertices with a discharging argument in suitable plane and projective-plane embeddings.