math.GT daily digest: 4 new submissions for 21 July 2026

New submissions

Annular Khovanov homology detects three-strand weaving links

• Authors: Suman Saurabh
• arXiv: 2607.16661
• Subjects: Geometric Topology (math.GT)
• Comments: 9 pages

For , let be the annular closure of . We prove that triply graded annular Khovanov homology over detects the underlying unoriented annular link . If , the only ambiguity is overall orientation reversal. If , the only ambiguity is independent reversal of components; every such reorientation has the same homology, so this is sharp. The proof combines braid detection from the extremal annular grading with a rigidity theorem: the Jones polynomial and exponent sum determine up to conjugacy in .

Khovanov homology and roll-spun slice disks

• Authors: Sang Woo Yoon
• arXiv: 2607.16837
• Subjects: Geometric Topology (math.GT)
• Comments: 53 pages, 68 figures

We show that Khovanov homology cannot distinguish the roll-spun slice disk from the trivial slice disk bounding the connected sum of a knot and its mirror when composed with a Morse 1-handle.

Proper Homotopy Nonrigidity of Open Contractible Manifolds

• Authors: Donghan Kim
• arXiv: 2607.18093
• Subjects: Geometric Topology (math.GT); Algebraic Topology (math.AT)
• Comments: 18 pages, 0 figures

Stallings' characterization of Euclidean space implies that the proper homotopy type of is topologically rigid for . We show that this phenomenon is exceptional. For every even integer , there exists a proper homotopy type containing infinitely many pairwise nonhomeomorphic smooth open contractible $N$-manifolds. More generally, let , and let $\pi$ be a finite superperfect group. If the reduced -eigenspace of the rational complex representation ring of $\pi$ is nonzero, then there exist infinitely many compact contractible smooth $N$-manifolds whose interiors are all properly homotopy equivalent but pairwise nonhomeomorphic. Their boundaries are homotopy equivalent integral homology -spheres with fundamental group $\pi$, but are pairwise not topologically $h$-cobordant.

Cross submissions

Sharp Weitzenböck and PIC2 Estimates from Sectional-Scalar Curvature Pinching

• Authors: Jian Ge
• arXiv: 2607.18216
• Cross-list from: Differential Geometry (math.DG)
• Subjects: Differential Geometry (math.DG); Geometric Topology (math.GT)

Let $V$ be an $n$-dimensional Euclidean vector space, ,where , and . We prove the sharp pointwise estimate [ q_2(E) \ge -\frac{2(\ell -1)}{3\ell} \mathrm{Scal}(E) \mathrm{Id}{\Lambda^2V^*} ] for every algebraic curvature tensor $E$ on $V$ with nonnegative sectional curvature. Applying this estimate to the decomposition , we obtain the vanishing of under a dimension-dependent strict sectional-scalar curvature pinching condition. At the weak endpoint, all harmonic two-forms are parallel. Apart from the flat case, this yields in odd dimensions and in even dimensions. At even-dimensional endpoint, forces $(M,g)$ to be isometric, up to scaling, to with its Fubini-Study metric. As a consequence every closed five-dimensional manifold satisfying the strict pinching condition implies a rational homology sphere. An anisotropic rescaling of the same homogeneous four-frame estimate also gives the sharp pointwise sectional-scalar pinching criterion [ K{\min} \ge \frac{n(n-1)}{n^2-n+12}S_0 \quad\Longrightarrow \mathrm{PIC2}. ] The strict pinching places the curvature tensor in the interior of PIC2 and normalized Ricci flow brings it to a positive constant sectional curvature.