The FAn Conjecture for Coxeter groups

Details The FAn Conjecture for Coxeter groups The FAn Conjecture for Coxeter groups

2005-09-19

arxiv.org/abs/math/0509439v3

Algebr. Geom. Topol. 6 (2006) 2117-2150

Mathematics

Group Theory

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

Scientific paper

10.2140/agt.2006.6.2117

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.

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