procongruence曲线复形与裤子复形的自同构

同构于拼接裤复形的共轭完成的扩展映射类群的自同构

Automorphisms of the procongruence pants complex

该研究证明了扩展映射类群的共轭完成的自同构均为内自同构，并展示了其与拼接裤复形自同构群的同构关系。

Mapping Class Groups and Interpolating Complexes: Rank

A family of interpolating graphs $\calC (S, ξ)$ of complexity $ξ$ is constructed for a surface $S$ and $-2 \leq ξ\leq ξ(S)$. For $ξ= -2, -1, ξ(S) -1$ these specialise to graphs quasi-isometric to the marking graph, the pants graph and the curve graph respectively. We generalise Theorems of Brock-Farb and Behrstock-Minsky to show that the rank of $\calC (S, ξ)$ is $r_ξ$, the largest number of disjoint copies of subsurfaces of complexity greater than $ξ$ that may be embedded in $S$. The interpolating graphs $\calC (S, ξ)$ interpolate between the pants graph and the curve graph.

不与曲线复形拟等距的双曲空间

Hyperbolic spaces not quasi-isometric to curve complexes

本文提出了一个判定条件，用于排除双曲空间与非例外曲面曲线复形拟等距的可能性，并证明了该结果适用于弧复形、圆盘复形等多种双曲复形。

A note on the connectivity of certain complexes associated to surfaces

This note is devoted to a trick which yields almost trivial proofs that certain complexes associated to topological surfaces are connected or simply connected. Applications include new proofs that the complexes of curves, separating curves, nonseparating curves, pants, and cut systems are all connected for genus $g \gg 0$. We also prove that two new complexes are connected : one involves curves which split a genus $2g$ surface into two genus $g$ pieces, and the other involves curves which are homologous to a fixed curve. The connectivity of the latter complex can be interpreted as saying the `…

标准曲面的远距和的 Kirby–Thompson 不变量

Kirby-Thompson invariants of distant sums of standard surfaces

本文计算标准曲面任意有限远距和的 L 与 L* 不变量，并给出桥数及两类不变量均可任意增大的纽结曲面首例。

曲面的拼布分解与Torelli群在扩展Hatcher复形上的作用

Quilt decompositions of surfaces and Torelli group action on the extended Hatcher complex

本文给出曲面拼布分解及带色拼布分解变换群胚的表示，通过构造二维胞腔复形实现，还证明Torelli群在这类复形上自由作用。