The FAn Conjecture for Coxeter groups

Barnhill, Angela Kubena¹

¹Department of Mathematics, The Ohio State University, 231 West 18th Avenue, Columbus, Ohio 43210, USA

Algebraic and Geometric Topology, Tome 6 (2006) no. 5, pp. 2117-2150

Résumé

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.

Détail

DOI : 10.2140/agt.2006.6.2117

Keywords: Coxeter group, fixed point, nonpositive curvature, triangle of groups, complex of groups

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