A topologically rigid set of quotients of the Davis complex

Abstract

A class of topological spaces is topologically rigid if for any pair of spaces in the class, an isomorphism on the level of fundamental groups induces a homeomorphism. 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 and introduce a topologically rigid subclass.