A very short proof of Forester's rigidity result

Details A very short proof of Forester's rigidity result A very short proof of Forester's rigidity result

2003-01-24

arxiv.org/abs/math/0301284v3

Geom. Topol. 7(2003) 321-328

Mathematics

Group Theory

Published by Geometry and Topology at http://www.maths.warwick.ac.uk/gt/GTVol7/paper10.abs.html

Scientific paper

The deformation space of a simplicial G-tree T is the set of G-trees which can be obtained from T by some collapse and expansion moves, or equivalently, which have the same elliptic subgroups as T. We give a short proof of a rigidity result by Forester which gives a sufficient condition for a deformation space to contain an Aut(G)-invariant G-tree. This gives a sufficient condition for a JSJ splitting to be invariant under automorphisms of G. More precisely, the theorem claims that a deformation space contains at most one strongly slide-free G-tree, where strongly slide-free means the following: whenever two edges e_1, e_2 incident on a same vertex v are such that G_{e_1} is a subset of G_{e_2}, then e_1 and e_2 are in the same orbit under G_v.

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