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Around a big mapping class group

Presented by: 
Juliette Bavard
Monday 19th June 2017 - 14:30 to 15:30
INI Seminar Room 1
Co-author: Alden Walker (Center for Communications Research, La Jolla)

The mapping class group of the plane minus a Cantor set naturally appears in many dynamical contexts, including group actions on surfaces, the study of groups of homeomorphisms on a Cantor set, and complex dynamics. In this talk, I will present the 'ray graph', which is a Gromov-hyperbolic graph on which this big mapping class group acts by isometries (it is an equivalent of the curve graph for this surface of infinite topological type). If time allows, I will explain how we can use this action to construct non trivial quasimorphisms on this group, although it is not acylindrically hyperbolic. This might involve joint work with Alden Walker.
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University of Cambridge Research Councils UK
    Clay Mathematics Institute London Mathematical Society NM Rothschild and Sons