Combinatorial conditions that imply word-hyperbolicity for 3-manifolds

层级双曲性的组合视角及其在映射类群商群中的应用

A combinatorial take on hierarchical hyperbolicity and applications to quotients of mapping class groups

本研究提出基于双曲单纯复形作用的层级双曲群组合判据，证明映射类群模Dehn扭大幂次的商群为层级双曲群，构造非初等双曲商群并将相关有限商问题归约为特定双曲群的剩余有限性问题。

A simple criterion for non-relative hyperbolicity and one-endedness of groups

We give a combinatorial criterion that implies both the non-strong relative hyperbolicity and the one-endedness of a finitely generated group. We use this to show that many important classes of groups do not admit a strong relatively hyperbolic group structure and have one end. Applications include surface mapping class groups, the Torelli group, (special) automorphism and outer automorphism groups of most free groups, and the three-dimensional Heisenberg group. Our final application is to Thompson's group F.

曲面上的球面正交环模式与修正组合全测地曲率

Spherical orthogonal ring patterns on surfaces and modified combinatorial total geodesic curvatures

研究闭曲面上球面正交环模式的刚性问题，通过修正Nie的组合全测地曲率并利用变分原理，证明了满足特定条件的闭曲面上球面正交环模式的刚性。

The mu vector, Morse inequalities and a generalized lower bound theorem for locally tame combinatorial manifolds

In a recent work [2] with Datta, we introduced the mu vector (with respect to a given field) of simplicial complexes and used it to study tightness and lower bounds. In this paper, we modify the definition of mu vectors. With the new definition, most results of [2] become correct without the hypothesis of 2-neighbourliness. In particular, the combinatorial Morse inequalities of [2] are now true of all simplicial complexes. As an application, we prove the following generalized lower bound theorem (GLBT) for connected locally tame combinatorial manifolds. If $M$ is such a manifold of dimension $…

Helly meets Garside and Artin

A graph is Helly if every family of pairwise intersecting combinatorial balls has a nonempty intersection. We show that weak Garside groups of finite type and FC-type Artin groups are Helly, that is, they act geometrically on Helly graphs. In particular, such groups act geometrically on spaces with convex geodesic bicombing, equipping them with a nonpositive-curvature-like structure. That structure has many properties of a CAT(0) structure and, additionally, it has a combinatorial flavor implying biautomaticity. As immediate consequences we obtain new results for FC-type Artin groups (in parti…