, Volume 175, Issue 3, pp 545-609
Date: 11 Nov 2008

Geometry of the mapping class groups I: Boundary amenability

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