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Contractibility of deformation spaces of G-trees

Matt Clay

Algebraic & Geometric Topology 5 (2005) 1481–1503

arXiv: math.GR/0511615

Abstract

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.

Keywords
$G$–tree, deformation space, Outer space
Mathematical Subject Classification 2000
Primary: 20E08
Secondary: 20F65, 20F28
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Publication
Received: 19 November 2004
Accepted: 20 October 2005
Published: 1 November 2005
Authors
Matt Clay
Department of Mathematics
University of Utah
Salt Lake City UT 84112-0090
USA