Thurston 脊的一个等变形变收缩
几何拓扑
2025-08-06 v5 群论
摘要
本文证明了闭可定向曲面的 Teichmüller 空间到一维数等于映射类群虚上同调维数的胞腔复形存在一个映射类群等变的形变收缩。该形变收缩的像包含于 Thurston 首次描述的 CW 复形——Thurston 脊——之中。Thurston 脊是 Teichmüller 空间中对应于双曲曲面的点的集合，这些双曲曲面的最短测地线（合腰曲线）将曲面切割成多边形。
引用
@article{arxiv.2211.03429,
title = {An equivariant deformation retraction of the Thurston spine},
author = {Ingrid Irmer},
journal= {arXiv preprint arXiv:2211.03429},
year = {2025}
}
备注
This paper was split into 3 pieces. The survey of Thurston's work is here "Thurston's deformation retraction of Teichm\"uller Space'', to appear in "In the Tradition of Thurston IV'' the second is "A matroid property of filling curves'' to appear in "Bulletin of the Australian Mathematical Society''. This version corresponds to the final chapter of the original paper