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Inventiones mathematicae

, Volume 215, Issue 2, pp 651–712 | Cite as

The Farrell–Jones Conjecture for mapping class groups

  • Arthur Bartels
  • Mladen BestvinaEmail author
Article

Abstract

We prove the Farrell–Jones Conjecture for mapping class groups. The proof uses the Masur–Minsky theory of the large scale geometry of mapping class groups and the geometry of the thick part of Teichmüller space. The proof is presented in an axiomatic setup, extending the projection axioms in Bestvina et al. (Publ Math Inst Hautes Études Sci 122:1–64, 2015). More specifically, we prove that the action of \({{\,\mathrm{Mod(\Sigma )}\,}}\) on the Thurston compactification of Teichmüller space is finitely \(\mathcal F\)-amenable for the family \({\mathcal {F}}\) consisting of virtual point stabilizers.

Mathematics Subject Classification

20F65 18F25 

Notes

Acknowledgements

Our collaboration started during a workshop at the Hausdorff Institute for Mathematics in Bonn in April 2015. We thank Wolfgang Lück for inviting us to this workshop. We thank Ken Bromberg, Jon Chaika, Howard Masur, and Kasra Rafi for many interesting conversations about Teichmüller theory. We especially thank Kasra Rafi for his help with Theorem 8.1. We thank the referee for a long list with helpful comments. The first author is supported by the SFB 878 in Münster. The second author is supported by the NSF under the Grant Number DMS-1308178.

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Authors and Affiliations

  1. 1.Mathematisches InstitutWWU MünsterMünsterGermany
  2. 2.Department of MathematicsUniversity of UtahSalt Lake CityUSA

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