Regular Isometries of CAT(0) Cube Complexes are Plentiful
Presenter
September 30, 2016
Keywords:
- CAT(0) space
- negative curvature manifolds
- Riemannian geometry
- amenable groups
- invariant ergodic measure
MSC:
- 57M60
- 57-xx
- 58-xx
- 58Dxx
- 58D05
- 58D19
Abstract
A rank-1 isometry of an irreducible CAT(0) space is an isometry that exhibits hyperbolic-type behavior regardless of whether the ambient space is indeed hyperbolic. A regular isometry of an (essential) CAT(0) cube complex is an isometry that is rank-1 in each irreducible factor. In a joint work with Lécureux and Mathéus, we study random walks and deduce that regular isometries are plentiful, provided the action is nonelementary. This generalizes previous results of Caprace-Sageev and Caprace-Zadnik (where it is assumed that the acting group has lattice-type properties).