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2003 A very short proof of Forester's rigidity result
Vincent Guirardel
Geom. Topol. 7(1): 321-328 (2003). DOI: 10.2140/gt.2003.7.321


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 e1,e2 incident on a same vertex v are such that Ge1Ge2, then e1 and e2 are in the same orbit under Gv.


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Vincent Guirardel. "A very short proof of Forester's rigidity result." Geom. Topol. 7 (1) 321 - 328, 2003.


Received: 24 January 2003; Revised: 11 April 2003; Accepted: 14 May 2003; Published: 2003
First available in Project Euclid: 21 December 2017

zbMATH: 1032.20018
MathSciNet: MR1988289
Digital Object Identifier: 10.2140/gt.2003.7.321

Primary: 20E08
Secondary: 20F65, 57M07

Rights: Copyright © 2003 Mathematical Sciences Publishers


Vol.7 • No. 1 • 2003
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