Constructing group actions on quasi-trees and applications to mapping class groups
Bestvina, Mladen1 ; Bromberg, Ken1 ; Fujiwara, Koji2
1 Department of Mathematics, University of Utah 84112 Salt Lake City UT USA
2 Department of Mathematics, Kyoto University 606-8502 Kyoto Japan
Publications Mathématiques de l'IHÉS, Tome 122 (2015), pp. 1-64.

A quasi-tree is a geodesic metric space quasi-isometric to a tree. We give a general construction of many actions of groups on quasi-trees. The groups we can handle include non-elementary (relatively) hyperbolic groups, CAT(0) groups with rank 1 elements, mapping class groups and Out(Fn). As an application, we show that mapping class groups act on finite products of δ-hyperbolic spaces so that orbit maps are quasi-isometric embeddings. We prove that mapping class groups have finite asymptotic dimension.

DOI : 10.1007/s10240-014-0067-4
Mots-clés : Asymptotic Dimension, Cayley Graph, Mapping Class Group, Hyperbolic Group, Cayley Tree
Bestvina, Mladen 1 ; Bromberg, Ken 1 ; Fujiwara, Koji 2

1 Department of Mathematics, University of Utah 84112 Salt Lake City UT USA
2 Department of Mathematics, Kyoto University 606-8502 Kyoto Japan 
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Bestvina, Mladen; Bromberg, Ken; Fujiwara, Koji. Constructing group actions on quasi-trees and applications to mapping class groups. Publications Mathématiques de l'IHÉS, Tome 122 (2015), pp. 1-64. doi : 10.1007/s10240-014-0067-4. https://www.numdam.org/articles/10.1007/s10240-014-0067-4/

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