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ISSN (electronic): 1472-2739
ISSN (print): 1472-2747
The $\mathrm{FA}_n$ Conjecture for Coxeter groups

Angela Kubena Barnhill

Algebraic & Geometric Topology 6 (2006) 2117–2150

arXiv: math.GR/0509439

Abstract

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

Keywords
Coxeter group, fixed point, nonpositive curvature, triangle of groups, complex of groups
Mathematical Subject Classification 2000
Primary: 20F65
Secondary: 20F55
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Publication
Received: 25 September 2005
Accepted: 6 March 2006
Published: 19 November 2006
Authors
Angela Kubena Barnhill
Department of Mathematics
The Ohio State University
231 West 18th Avenue
Columbus, Ohio 43210
USA