Algebraic & Geometric Topology

Contractibility of deformation spaces of G-trees

Matt Clay

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Forester has defined spaces of simplicial tree actions for a finitely generated group, called deformation spaces. Culler and Vogtmann’s Outer space is an example of a deformation space. Using ideas from Skora’s proof of the contractibility of Outer space, we show that under some mild hypotheses deformation spaces are contractible.

Article information

Algebr. Geom. Topol., Volume 5, Number 4 (2005), 1481-1503.

Received: 19 November 2004
Accepted: 20 October 2005
First available in Project Euclid: 20 December 2017

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 20E08: Groups acting on trees [See also 20F65]
Secondary: 20F65: Geometric group theory [See also 05C25, 20E08, 57Mxx] 20F28: Automorphism groups of groups [See also 20E36]

$G$–tree deformation space Outer space


Clay, Matt. Contractibility of deformation spaces of G-trees. Algebr. Geom. Topol. 5 (2005), no. 4, 1481--1503. doi:10.2140/agt.2005.5.1481.

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