Thurston 骨架的等变形变收缩

Thurston 脊的 Morse-Smale 性质

The Morse-Smale Property of the Thurston Spine

本文研究 Thurston 脊的局部性质及其光滑片段，证明其满足与带边流形上 Morse 函数的 Morse-Smale 复形类似的性质。

Teichmüller 曲线中的 Thurston 脊

Thurston spine in a Teichmüller curve

该研究通过构造 Teichmüller 曲线刻画其与 Thurston 脊的交，证明该交为三叉树且是等变形变收缩核，并由此获得多种本质环。

The Thurston metric on hyperbolic domains and boundaries of convex hulls

We show that the nearest point retraction is a uniform quasi-isometry from the Thurston metric on a hyperbolic domain in the Riemann sphere to the boundary of the convex hull of its complement. As a corollary, one obtains explicit bounds on the quasi-isometry constant of the nearest point retraction with respect to the Poincare metric when the domain is uniformly perfect. We also establish Marden and Markovic's conjecture that a hyperbolic domain is uniformly perfect if and only if the nearest point retraction is Lipschitz with respect to the Poincare metric.

Thurston 脊柱与亏格 2 中的等变胞腔分解

The Thurston spine and equivariant cell decompositions in genus 2

本文构造了亏格 2 Teichmüller 空间的 Thurston 脊柱，识别了所有填充 systole 集合的映射类群轨道，并与基于 Rivin 角坐标的胞腔分解进行了对比。

估计 Thurston 脊的维数

Estimating the dimension of Thurston spine

本文研究了 Thurston 脊 Pg 的余维数性质，证明了存在无限整数集 A 使得当亏格 g 在 A 中变化时 codim Pg 为 o(g/ log g)，从而验证了 M. Fortier Bourque 的猜想。

Thurston 脊柱的维数

The dimension of Thurston's spine

本文证明存在亏格 $g$ 使得闭双曲曲面中 systole 填满的集合维数至少 $(5-\varepsilon)g$，从而该脊柱维数超过映射类群的虚拟上同调维数。