Deformation spaces of trees

Details Deformation spaces of trees Deformation spaces of trees

2006-05-19

arxiv.org/abs/math/0605545v2

Groups, Geometry, and Dynamics. Volume 1, Issue 2, 2007, pp. 135-181

Mathematics

Group Theory

Update to published version. 43 pages

Scientific paper

Let G be a finitely generated group. Two simplicial G-trees are said to be in the same deformation space if they have the same elliptic subgroups (if H fixes a point in one tree, it also does in the other). Examples include Culler-Vogtmann's outer space, and spaces of JSJ decompositions. We discuss what features are common to trees in a given deformation space, how to pass from one tree to all other trees in its deformation space, and the topology of deformation spaces. In particular, we prove that all deformation spaces are contractible complexes.

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