Videos

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).
Supplementary Materials