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Constructing group actions on quasi-trees and applications to mapping class groups

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Abstract

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(F n ). 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.

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Authors and Affiliations

  1. Department of Mathematics, University of Utah, Salt Lake City, UT, 84112, USA

    Mladen Bestvina & Ken Bromberg

  2. Department of Mathematics, Kyoto University, Kyoto, 606-8502, Japan

    Koji Fujiwara

Authors
  1. Mladen Bestvina
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  2. Ken Bromberg
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  3. Koji Fujiwara
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Corresponding author

Correspondence to Koji Fujiwara.

Additional information

The first two authors gratefully acknowledge the support by the National Science Foundation. The third author is supported in part by Grant-in-Aid for Scientific Research (No. 23244005).

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Bestvina, M., Bromberg, K. & Fujiwara, K. Constructing group actions on quasi-trees and applications to mapping class groups. Publ.math.IHES 122, 1–64 (2015). https://doi.org/10.1007/s10240-014-0067-4

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