Regular Isometries of CAT(0) Cube Complexes are Plentiful
Groups acting on CAT(0) spaces September 27, 2016 - September 30, 2016
CAT(0) space
negative curvature manifolds
Riemannian geometry
amenable groups
invariant ergodic measure
57-XX - Manifolds and cell complexes {For complex manifolds, see 32Qxx}
58D05 - Groups of diffeomorphisms and homeomorphisms as manifolds [See also 22E65, 57S05]
14620
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).
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