A topologically rigid set of quotients of the Davis complex
Geometric Topology
2023-09-21 v2 Group Theory
Abstract
A class of topological spaces is topologically rigid if any two spaces with the same fundamental group are also homeomorphic. Topological rigidity, in addition to its intrinsic interest, has been useful for solving abstract commensurability questions. In this paper, we explore the topological rigidity of quotients of the Davis complex of certain right angled Coxeter groups by providing conditions on the defining graphs that obstruct topological rigidity. Furthermore, we explore why topological rigidity is hard to achieve for quotients of the Davis complex. Nonetheless, we conclude by introducing infinitely many infinite topologically rigid subclasses.
Keywords
Cite
@article{arxiv.2204.12028,
title = {A topologically rigid set of quotients of the Davis complex},
author = {Yandi Wu},
journal= {arXiv preprint arXiv:2204.12028},
year = {2023}
}
Comments
19 pages, 10 figures