N-step energy of maps and fixed-point property of random groups
Differential Geometry
2012-10-23 v1 Group Theory
Abstract
We prove that a random group of the graph model associated with a sequence of expanders has fixed-point property for a certain class of CAT(0) spaces. We use Gromov's criterion for fixed-point property in terms of the growth of n-step energy of equivariant maps from a finitely generated group into a CAT(0) space, to which we give a detailed proof. We estimate a relevant geometric invariant of the tangent cones of the Euclidean buildings associated with the groups PGL(m,Q_r), and deduce from the general result above that the same random group has fixed-point property for all of these Euclidean buildings with m bounded from above.
Keywords
Cite
@article{arxiv.1210.5829,
title = {N-step energy of maps and fixed-point property of random groups},
author = {Hiroyasu Izeki and Takefumi Kondo and Shin Nayatani},
journal= {arXiv preprint arXiv:1210.5829},
year = {2012}
}