Fixed points for actions of Aut(Fn) on CAT(0) spaces
Group Theory
2016-03-04 v4 Metric Geometry
Abstract
For n greater or equal 4 we discuss questions concerning global fixed points for isometric actions of Aut(Fn), the automorphism group of a free group of rank n, on complete CAT(0) spaces. We prove that whenever Aut(Fn) acts by isometries on complete d-dimensional CAT(0) space with d is less than 2 times the integer function of n over 4 and minus 1, then it must fix a point. This property has implications for irreducible representations of Aut(Fn), which are also presented here. For SAut(Fn), the unique subgroup of index two in Aut(Fn), we obtain similar results.
Cite
@article{arxiv.1112.5014,
title = {Fixed points for actions of Aut(Fn) on CAT(0) spaces},
author = {Olga Varghese},
journal= {arXiv preprint arXiv:1112.5014},
year = {2016}
}