Geodesic
Embedding mapping class groups into a finite product of trees
David Hume1
1UC Louvain, Louvain-La-Neuve, Belgium
Groups, geometry, and dynamics, Tome 11 (2017) no. 2, pp. 613-647

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DOI

We prove the equivalence between a relative bottleneck property and being quasi-isometric to a tree-graded space. As a consequence, we deduce that the quasi-trees of spaces defined axiomatically by Bestvina-Bromberg-Fujiwara are quasi-isometric to tree-graded spaces. Using this we prove that mapping class groups quasi-isometrically embed into a finite product of simplicial trees. In particular, these groups have finite Assouad–Nagata dimension, direct embeddings exhibiting lp compression exponent 1 for all p≥1 and they quasi-isometrically embed into l1(N). We deduce similar consequences for relatively hyperbolic groups whose parabolic subgroups satisfy such conditions.
DOI : 10.4171/ggd/410
Classification : 20-XX
Mots-clés : Tree-graded space, quasi-tree, embeddings, mapping class group, curve complex

David Hume  1

1 UC Louvain, Louvain-La-Neuve, Belgium 
David Hume. Embedding mapping class groups into a finite product of trees. Groups, geometry, and dynamics, Tome 11 (2017) no. 2, pp. 613-647. doi: 10.4171/ggd/410
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     journal = {Groups, geometry, and dynamics},
     pages = {613--647},
     year = {2017},
     volume = {11},
     number = {2},
     doi = {10.4171/ggd/410},
     url = {http://geodesic.mathdoc.fr/articles/10.4171/ggd/410/}
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