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Around a big mapping class group

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NPCW05 - Group actions and cohomology in non-positive curvature

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.

This talk is part of the Isaac Newton Institute Seminar Series series.

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