Geometry of the mapping class groups I: Boundary amenability

By Ursula Hamenstädt. 2005

105 citations recorded by the source corpus.

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 $\mathcal{M}\mathcal{C}\mathcal{G}$.

Subfields: Applied Mathematics, Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/510c07c3dd83b007e01893ae81bf92559cd20981

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In Applied Mathematics

In Geometry and Topology

In Mathematical Physics

Citations in the corpus

Geometry of the complex of curves and of Teichmüller space (2005, background): “Section 2 introduces train tracks, geodesic laminations and quadratic differentials and summarizes some of their properties.”
The asymptotic dimension of a curve graph is finite (2005, background): “It was recently shown that Mod(S) is exact [21, 32].”
The Mapping Class Group from the Viewpoint of Measure Equivalence Theory (2005, methodology): “After we finished to write the first draft of this paper, we found the paper [39] related to Theorem 1.”
The geometry of the disk complex (2010, background): “Since τ fixes X setwise, it cannot fix any boundary component of X; thus X is a twice-holed torus and X/τ is a once-holed Klein bottle.”