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Inventiones mathematicae

, Volume 175, Issue 3, pp 545–609 | Cite as

Geometry of the mapping class groups I: Boundary amenability

  • Ursula Hamenstädt
Article

Abstract

We construct a geometric model for the mapping class group \(\mathcal{M}\mathcal{C}\mathcal{G}\) of a non-exceptional oriented surface S of genus g with k punctures and use it to show that the action of \(\mathcal{M}\mathcal{C}\mathcal{G}\) on the compact metrizable Hausdorff space of complete geodesic laminations for S is topologically amenable. As a consequence, the Novikov higher signature conjecture holds for every subgroup of \(\mathcal{M}\mathcal{C}\mathcal{G}\).

Keywords

Mapping Class Group Large Branch Dehn Twist Train Track Splitting Sequence 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag 2008

Authors and Affiliations

  1. 1.Mathematisches Institut der Universität BonnBonnGermany

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