Algebraic & Geometric Topology

The $\mathrm{FA}_n$ Conjecture for Coxeter groups

Angela Kubena Barnhill

Full-text: Open access

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.

Article information

Source
Algebr. Geom. Topol., Volume 6, Number 5 (2006), 2117-2150.

Dates
Received: 25 September 2005
Accepted: 6 March 2006
First available in Project Euclid: 20 December 2017

Permanent link to this document
https://projecteuclid.org/euclid.agt/1513796631

Digital Object Identifier
doi:10.2140/agt.2006.6.2117

Mathematical Reviews number (MathSciNet)
MR2263060

Zentralblatt MATH identifier
1173.20317

Subjects
Primary: 20F65: Geometric group theory [See also 05C25, 20E08, 57Mxx]
Secondary: 20F55: Reflection and Coxeter groups [See also 22E40, 51F15]

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

Citation

Barnhill, Angela Kubena. The $\mathrm{FA}_n$ Conjecture for Coxeter groups. Algebr. Geom. Topol. 6 (2006), no. 5, 2117--2150. doi:10.2140/agt.2006.6.2117. https://projecteuclid.org/euclid.agt/1513796631


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