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Geometry of the mapping class groups I: Boundary amenability

Research paper by Ursula Hamenstaedt

Indexed on: 19 Mar '08Published on: 19 Mar '08Published in: Mathematics - Group Theory



Abstract

We construct a geometric model for the mapping class group M of a non-exceptional oriented surface of finite type and use it to show that the action of M on the compact Hausdorff space of complete geodesic laminations is topologically amenable. As a consequence, the Novikov higher signature conjecture holds for every subgroup of M.