拓扑学中的组合与几何方法
几何拓扑
2011-01-18 v1
摘要
从决定通过将八面体的面两两粘合可以获得多少种不同拓扑空间这一（看似）初等的问题出发，我们将描述双曲几何在三维拓扑学中所扮演的核心角色。我们还将指出其与二维情形的显著差异，并回顾过去几年不同数学家开发的针对三维流形的组合与计算方法的某些结果。
引用
@article{arxiv.0706.4368,
title = {Combinatorial and geometric methods in topology},
author = {Carlo Petronio and Damian Heard and Ekaterina Pervova},
journal= {arXiv preprint arXiv:0706.4368},
year = {2011}
}
评论
This expository paper is the text of a conference given by the author to a broad audience of mathematicians. An upcoming article will contain more detailed proofs and an accurate description of the hyperbolic and non-hyperbolic orientable manifolds obtained by gluing together in pairs the faces of the octahedron. Appendix by Damian Heard and Ekaterina Pervova