math.GT daily digest: 7 new submissions for 19 August 2026

New submissions

An exotic and an exotic

• Authors: Bernd Johannes Wuebben
• arXiv: 2608.17267
• Subjects: Geometric Topology (math.GT)
• Comments: 32 pages, 2 figures

We prove that a specified Lidman-Piccirillo piece $V$, a symplectic $4$-manifold with the homology of built from a genus-$2$ surface bundle over a once-punctured torus by two Luttinger surgeries, is simply connected, for an explicit permitted choice of the two surgery parametrizations. Three consequences follow. The symplectic double is homeomorphic but not diffeomorphic to . The Lidman-Piccirillo manifolds $B$ and $W$ are homeomorphic. Since the figure-eight knot is slice in $B$ and not in $W$, they are the first pair of homeomorphic closed $4$-manifolds distinguished by unconstrained knot slicing, that is, by sliceness with no constraint on the homology class of the slice disk; detecting smooth structure this way goes back to Casson. Finally, the regluing of Lidman and Piccirillo's Theorem~2 applied to $Z$ yields a closed simply connected $4$-manifold homeomorphic but not diffeomorphic to . The consequences follow from the simple-connectivity statement by the classifications of Freedman and of Hambleton-Kreck, together with a rigidity analysis of the surgery parameters. The fundamental group is computed in the style of Baldridge and Kirk, from explicit based representatives of every meridian and Lagrangian push off, and the resulting relation system is decided by coset enumeration, after calibration on two configurations whose answers are known independently. The development calculations and finite-presentation decisions can be reproduced from the ancillary files.

Infinite order corks that admit Stein structures

• Authors: Yikai Teng
• arXiv: 2608.17462
• Subjects: Geometric Topology (math.GT)
• Comments: 18 pages, 38 figures. All comments are welcome

In this paper, we construct an infinite family of infinite order corks admitting Stein structures. This answers a question raised by Akbulut and Gompf.

The first Galois obstruction in the Johnson cokernel

• Authors: Shigeyuki Morita, Takuya Sakasai, Masaaki Suzuki
• arXiv: 2608.17673
• Subjects: Geometric Topology (math.GT); Algebraic Topology (math.AT)
• Comments: 28 pages

We explicitly determine the first Galois obstruction in the cokernel of the Johnson homomorphism of the mapping class group of a surface of genus $g$, for every genus . It is described as a sum of two terms which are considerably different in character. One lies in the kernel of the Enomoto-Satoh trace map, whereas the other belongs to a certain ideal which vanishes upon passage to the closed surface case.

Cross submissions

Small Cancellation Stability and Isomorphism Rigidity for Generic Finitely Presented Groups

• Cross-list from: math.GR
• Authors: Ilya Kapovich
• arXiv: 2608.17238
• Subjects: Group Theory (math.GR); Geometric Topology (math.GT)

Let with , and fix . For every fixed , we prove that a $q$-tuple of independent uniformly random cyclically reduced words of length $n$ is \emph{$\lambda$-stable} with probability converging to $1$ exponentially fast. Namely, for every , the tuple , after cyclic reduction and symmetrization, satisfies the small cancellation condition.

Combining generic $\lambda$-stability with Greendlinger normal-closure rigidity and with previous results of Kapovich-Schupp-Shpilrain on generic Nielsen uniqueness and generic Whitehead rigidity we establish, for any fixed , isomorphism rigidity for generic $m$-generator $q$-relator groups. Thus we show that two such generic groups and are isomorphic if and only if, after possibly permuting and inverting the generators , the relator tuples and are the same, up to reordering, cyclic permutations and inverting the relators. Among the applications, we obtain a quadratic-time algorithm that generically solves the isomorphism problem for $m$-generator $q$-relator groups, and show that the number of isomorphism types represented by $m$-generator $q$-relator presentations with cyclically reduced relators of length $n$ is asymptotic to [ \frac{(2m-1)^{qn}}{2^{m+q}m!,q!,n^q}. ]

The proof of generic $\lambda$-stability relies on the use of geodesic currents and on our deterministic sufficient criterion for a $q$-tuple $\mathbb{W}$ in to be $\lambda$-stable in terms of the components of $\mathbb{W}$ being sufficiently projectively close to filling currents.

Simplicial Volume and Scalar Curvature on Closed Kähler Surfaces

• Cross-list from: math.DG
• Authors: Jie Min, Fangyang Zheng, Bo Zhu
• arXiv: 2608.17335
• Subjects: Differential Geometry (math.DG); Geometric Topology (math.GT); Symplectic Geometry (math.SG)
• Comments: 23 pages. Comments are welcome!

Let $M$ be a closed Kähler surface. We prove that every Riemannian metric $g$ on $M$ with , where , satisfies $$ \lVert M\rVert\leq \frac{27}{2},\lambda^4\operatorname{vol}_g(M). $$ This proves Gromov's quantitative scalar-curvature--simplicial-volume conjecture for closed Kähler surfaces. We also construct infinitely many non-Kähler symplectic 4-manifolds of general type with positive simplicial volume for which the same estimate holds.

On the degrees of equivariant maps from spheres to complex Stiefel manifolds

• Cross-list from: math.AT
• Authors: Haibao Duan, Ruizhi Huang
• arXiv: 2608.17752
• Subjects: Algebraic Topology (math.AT); Geometric Topology (math.GT)
• Comments: 21 pages; this article is dedicated to Fred Cohen and is submitted to the proceedings of the Fields program in honour of Fred Cohen

We study the set of degrees of $\mathbb{Z}/m$-equivariant maps from spheres to complex Stiefel manifolds, motivated by the work of Astey--Gitler--Micha--Pastor. Under a suitable arithmetic condition, this set is determined using results of James, Atiyah--Todd, and Adams--Walker. Our approach is homotopy-theoretic.

Normal Curvature and the Projective Systole

• Cross-list from: math.DG
• Authors: Tsz-Kiu Aaron Chow, Jingbo Wan
• arXiv: 2608.18002
• Subjects: Differential Geometry (math.DG); Geometric Topology (math.GT)

For a smooth immersion , we observe that the sharp systolic inequality forces a sharp lower bound on its maximal normal curvature $\kappa (F)$. In dimensions , the sharp inequalities of Pu and Bray--Brendle--Eichmair--Neves therefore give . Equality holds precisely for the Veronese embedding. This recovers Petrunin's theorem for and, for , confirms the first open case of his question for real projective spaces.