The FAn Conjecture for Coxeter groups

Abstract

We study global fixed points for actions of Coxeter groups on nonpositively curved singular spaces. In particular, we consider property FA_n, an analogue of Serre's property FA for actions on CAT(0) complexes. Property FA_n has implications for irreducible representations and complex of groups decompositions. In this paper, we give a specific condition on Coxeter presentations that implies FA_n and show that this condition is in fact equivalent to FA_n for n=1 and 2. As part of the proof, we compute the Gersten-Stallings angles between special subgroups of Coxeter groups.

This is the version published by Algebraic & Geometric Topology on 19 November 2006

References in corpus (1)

• Group actions and Helly's theorem

Cited by in corpus (5)

• Infinite groups with fixed point properties
• Low-dimensional representations of matrix groups and group actions on CAT(0) spaces and manifolds
• Group actions and Helly's theorem
• Fixed points for actions of Aut(Fn) on CAT(0) spaces
• Rigidity of matrix group actions on CAT(0) spaces with possible parabolic isometries and uniquely arcwise connected spaces