# zbMATH — the first resource for mathematics

Contractibility of deformation spaces of $$G$$-trees. (English) Zbl 1120.20027
Summary: 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.
Reviewer: Reviewer (Berlin)

##### MSC:
 20E08 Groups acting on trees 20F65 Geometric group theory 20F28 Automorphism groups of groups 57M07 Topological methods in group theory
Full Text:
##### References:
 [1] M Bestvina, The topology of $$\mathrm{Out}(F_n)$$, Higher Ed. Press (2002) 373 · Zbl 1060.57002 [2] M R Bridson, K Vogtmann, Automorphism groups of free groups, surface groups and free abelian groups, Proc. Sympos. Pure Math. 74, Amer. Math. Soc. (2006) 301 · Zbl 1184.20034 [3] M Culler, J W Morgan, Group actions on $$\mathbbR$$-trees, Proc. London Math. Soc. $$(3)$$ 55 (1987) 571 · Zbl 0658.20021 · doi:10.1112/plms/s3-55.3.571 [4] M Culler, K Vogtmann, Moduli of graphs and automorphisms of free groups, Invent. Math. 84 (1986) 91 · Zbl 0589.20022 · doi:10.1007/BF01388734 · eudml:143335 [5] M Forester, Deformation and rigidity of simplicial group actions on trees, Geom. Topol. 6 (2002) 219 · Zbl 1118.20028 · doi:10.2140/gt.2002.6.219 · emis:journals/UW/gt/GTVol6/paper8.abs.html · eudml:127788 · arxiv:math/0107008 [6] M Gromov, Groups of polynomial growth and expanding maps, Inst. Hautes Études Sci. Publ. Math. (1981) 53 · Zbl 0474.20018 · doi:10.1007/BF02698687 · numdam:PMIHES_1981__53__53_0 · eudml:103974 [7] V Guirardel, G Levitt, A general construction of JSJ decompositions, Trends Math., Birkhäuser (2007) 65 · Zbl 1162.20017 [8] V Guirardel, G Levitt, The outer space of a free product, Proc. Lond. Math. Soc. $$(3)$$ 94 (2007) 695 · Zbl 1168.20011 · doi:10.1112/plms/pdl026 [9] D McCullough, A Miller, Symmetric automorphisms of free products, Mem. Amer. Math. Soc. 122 (1996) · Zbl 0860.20029 [10] F Paulin, The Gromov topology on $$\mathbbR$$-trees, Topology Appl. 32 (1989) 197 · Zbl 0675.20033 · doi:10.1016/0166-8641(89)90029-1 [11] R Skora, Deformation of length functions in groups, preprint · Zbl 0607.57008 [12] K Vogtmann, Automorphisms of free groups and outer space (2002) 1 · Zbl 1017.20035 · doi:10.1023/A:1020973910646
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.