The RAAGs on the complement graphs of path graphs in mapping class groups

Path lifting properties and embedding between RAAGs

For a finite simplicial graph $Γ$, let $G(Γ)$ denote the right-angled Artin group on the complement graph of $Γ$. In this article, we introduce the notions of "induced path lifting property" and "semi-induced path lifting property" for immersions between graphs, and obtain graph theoretical criteria for the embedability between right-angled Artin groups. We recover the result of S.-h.{} Kim and T.{} Koberda that an arbitrary $G(Γ)$ admits a quasi-isometric group embedding into $G(T)$ for some finite tree $T$. The upper bound on the number of vertices of $T$ is improved from $2^{2^{(m-1)^2}}$ t…

右角Artin群的拟等距分类II：若干无限外自同构群情形

Quasi-isometry classification of right-angled Artin groups II: several infinite out cases

针对哪类右角Artin群（RAAG）的拟等距分类与可公度分类一致的问题，本文确定两类外自同构群含相邻平延和部分共轭的无限RAAG，证明其拟等距等价于可公度，提出基于定义图的判断算法，并通过形变论证和立方化技术解决重构映射问题。

所有映射类群和右角群的一族粗中位数结构

A continuum of coarse medians for all mapping class groups and right-angled groups

本文证明非零星曲面映射类群及一大类右角群具有一族等变粗中位数结构，通过拟上循环修改层级双曲群结构，改进先前定理且不依赖余紧立方化。

Asymptotics of quantum invariants of surface diffeomorphisms II: The figure-eight knot complement

In earlier work, the authors introduced a conjecture which, for an orientation-preserving diffeomorphism $φ\colon S \to S$ of a surface, connects a certain quantum invariant of $φ$ with the hyperbolic volume of its mapping torus $M_φ$. This article provides a proof of this conjecture in the simplest case where it applies, namely when the surface $S$ is the one-puncture torus and the mapping torus $M_φ$ is the complement of the figure-eight knot.

映射类群在正亏格黎曼曲面有限子集补空间的基本群上的作用

The action of the Mapping Class Group on the fundamental group of the complement of a finite subset of a Riemann surface of positive genus

本文通过将映射类群 $M(g,n)$ 生成元的像计算为基本群的外自同构，描述了该群在具有 $n$ 个标记点的正亏格紧致可定向拓扑曲面 $T_{g,n}$ 基本群上的作用。

A presentation for the mapping class group of a non-orientable surface from the action on the complex of curves

We study the action of the mapping class group M(F) on the complex of curves of a non-orientable surface F. We obtain, by using a result of K. S. Brown, a presentation for M(F) defined in terms of the mapping class groups of the complementary surfaces of collections of curves, provided that F is not sporadic, i.e. the complex of curves of F is simply connected. We also compute a finite presentation for the mapping class group of each sporadic surface.