Inventiones mathematicae

, Volume 175, Issue 3, pp 545–609

Geometry of the mapping class groups I: Boundary amenability


DOI: 10.1007/s00222-008-0158-2

Cite this article as:
Hamenstädt, U. Invent. math. (2009) 175: 545. doi:10.1007/s00222-008-0158-2


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

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© Springer-Verlag 2008

Authors and Affiliations

  1. 1.Mathematisches Institut der Universität BonnBonnGermany