Algebraic & Geometric Topology

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

Angela Kubena Barnhill

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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

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

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

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

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

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


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.

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