Inventiones mathematicae

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

Geometry of the mapping class groups I: Boundary amenability

  • Ursula Hamenstädt


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 \(\mathcal{M}\mathcal{C}\mathcal{G}\).


Mapping Class Group Large Branch Dehn Twist Train Track Splitting Sequence 
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© Springer-Verlag 2008

Authors and Affiliations

  1. 1.Mathematisches Institut der Universität BonnBonnGermany

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