Geodesic
Contractibility of deformation spaces of G-trees
Clay, Matt1
1Department of Mathematics, University of Utah, Salt Lake City UT 84112-0090, USA
Algebraic and Geometric Topology, Tome 5 (2005) no. 4, pp. 1481-1503
Cet article a éte moissonné depuis la source Mathematical Sciences Publishers

Voir la notice de l'article

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.

DOI : 10.2140/agt.2005.5.1481
Keywords: $G$–tree, deformation space, Outer space

Clay, Matt  1

1 Department of Mathematics, University of Utah, Salt Lake City UT 84112-0090, USA 
@article{10_2140_agt_2005_5_1481,
     author = {Clay, Matt},
     title = {Contractibility of deformation spaces of {G-trees}},
     journal = {Algebraic and Geometric Topology},
     pages = {1481--1503},
     year = {2005},
     volume = {5},
     number = {4},
     doi = {10.2140/agt.2005.5.1481},
     url = {http://geodesic.mathdoc.fr/articles/10.2140/agt.2005.5.1481/}
}
TY  - JOUR
AU  - Clay, Matt
TI  - Contractibility of deformation spaces of G-trees
JO  - Algebraic and Geometric Topology
PY  - 2005
SP  - 1481
EP  - 1503
VL  - 5
IS  - 4
UR  - http://geodesic.mathdoc.fr/articles/10.2140/agt.2005.5.1481/
DO  - 10.2140/agt.2005.5.1481
ID  - 10_2140_agt_2005_5_1481
ER  - 
%0 Journal Article
%A Clay, Matt
%T Contractibility of deformation spaces of G-trees
%J Algebraic and Geometric Topology
%D 2005
%P 1481-1503
%V 5
%N 4
%U http://geodesic.mathdoc.fr/articles/10.2140/agt.2005.5.1481/
%R 10.2140/agt.2005.5.1481
%F 10_2140_agt_2005_5_1481
Clay, Matt. Contractibility of deformation spaces of G-trees. Algebraic and Geometric Topology, Tome 5 (2005) no. 4, pp. 1481-1503. doi: 10.2140/agt.2005.5.1481

[1] M Bestvina, The topology of $\mathrm{Out}(F_n)$, from: "Proceedings of the International Congress of Mathematicians, Vol II (Beijing, 2002)", Higher Ed. Press (2002) 373

[2] M R Bridson, K Vogtmann, Automorphism groups of free groups, surface groups and free abelian groups, from: "Problems on mapping class groups and related topics", Proc. Sympos. Pure Math. 74, Amer. Math. Soc. (2006) 301

[3] M Culler, J W Morgan, Group actions on $\mathbb{R}$–trees, Proc. London Math. Soc. $(3)$ 55 (1987) 571

[4] M Culler, K Vogtmann, Moduli of graphs and automorphisms of free groups, Invent. Math. 84 (1986) 91

[5] M Forester, Deformation and rigidity of simplicial group actions on trees, Geom. Topol. 6 (2002) 219

[6] M Gromov, Groups of polynomial growth and expanding maps, Inst. Hautes Études Sci. Publ. Math. (1981) 53

[7] V Guirardel, G Levitt, A general construction of JSJ decompositions, from: "Geometric group theory", Trends Math., Birkhäuser (2007) 65

[8] V Guirardel, G Levitt, The outer space of a free product, Proc. Lond. Math. Soc. $(3)$ 94 (2007) 695

[9] D Mccullough, A Miller, Symmetric automorphisms of free products, Mem. Amer. Math. Soc. 122 (1996)

[10] F Paulin, The Gromov topology on $\mathbb{R}$–trees, Topology Appl. 32 (1989) 197

[11] R Skora, Deformation of length functions in groups, preprint

[12] K Vogtmann, Automorphisms of free groups and outer space, from: "Proceedings of the Conference on Geometric and Combinatorial Group Theory, Part I (Haifa, 2000)" (2002) 1

Cité par Sources :