## A very short proof of Forester’s rigidity result.(English)Zbl 1032.20018

Let $$G$$ be a group and let $$T$$ be a $$G$$-tree. If $$v$$ (respectively $$e$$) is a vertex (respectively edge) of $$T$$ let $$G_v$$ (respectively $$G_e$$) be the stabilizer of $$v$$ (respectively of $$e$$). Then $$T$$ is strongly slide-free if whenever $$e_1,e_2$$ are two edges having a common vertex $$v$$ and are such that $$G_{e_1}\subset G_{e_2}$$ then $$e_1$$ and $$e_2$$ are in the same orbit under $$G_v$$. The deformation space of $$T$$ is the set of $$G$$-trees which can be deformed into $$T$$. In this paper there is given a short proof of a theorem of M. Forester [Geom. Topol. 6, 219-267 (2002)] that for each deformation space there is at most one strongly slide-free minimal $$G$$-tree. The spirit of the proof comes from a paper of N. D. Gilbert, J. Howie, V. Metaftsis and E. Raptis [J. Group Theory 3, No. 2, 213-223 (2000; Zbl 0979.20027)].
Reviewer: J.D.Dixon (Ottawa)

### MSC:

 20E08 Groups acting on trees 57M07 Topological methods in group theory 20F65 Geometric group theory

Zbl 0979.20027
Full Text:

### References:

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