The rigidity of Coxeter groups
Abstract: It is well-known that negatively curved manifolds can be essentially recovered from their fundamental groups alone (by Mostow rigidity). Coxeter groups are a large class of fairly well-behaved groups which act on spaces called Coxeter complexes which are singular spaces of nonpositive curvature. Thus a natural question is "to what extent can the Coxeter complex of a Coxeter group be recovered from the group itself?" In this talk I will survey what is known about various types of rigidity for these groups as well as presenting some new non-rigidity results which are joint work with Noel Brady, Walter Neumann, and Bernhard Muehlherr.