Volume 5, issue 4 (2005)

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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