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Curve Graphs and Surface Diffeomorphism Groups

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We will discuss a new type of curve graph and apply it to the study of surface diffeomorphism and homeomorphism groups. On the one hand, we will present a construction (joint with Jonathan Bowden and Richard Webb) of nontrivial quasimorphisms on the group of diffeomorphisms of a surface of genus at least 1 which are isotopic to the identity. As a consequence, this solves a question by Burago-Ivanov-Polterovich on the unboundedness of the fragmentation norm. I will also talk about work in progress (joint additionally with Katie Mann and Emmanuel Militon) which begins to develop a dictionary between the dynamics of torus homeomorphisms and their action on the new curve graph.

This talk is part of the Geometric Group Theory (GGT) Seminar series.

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