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• W1818484544 abstract "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 $ell^p$ compression exponent $1$ for all $pgeq 1$ and they quasi-isometrically embed into $ell^1(mathbb N)$. We deduce similar consequences for relatively hyperbolic groups whose parabolic subgroups satisfy such conditions. In obtaining these results we also demonstrate that curve complexes of compact surfaces and coned-off graphs of relatively hyperbolic groups admit quasi-isometric embeddings into finite products of trees." @default.
• W1818484544 created "2016-06-24" @default.
• W1818484544 creator A5016975501 @default.
• W1818484544 date "2012-07-09" @default.
• W1818484544 modified "2023-09-27" @default.
• W1818484544 title "Embedding mapping class groups into finite products of trees" @default.
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