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Seminar

RAS - Research Seminar (Part 1): Quasi-morphisms on surface diffeomorphism groups October 05, 2020 (09:00 AM PDT - 10:00 AM PDT)
Parent Program:
Location: MSRI: Online/Virtual
Speaker(s) Sebastian Hensel (LMU München)
Description

To participate in this seminar, please register here: https://www.msri.org/seminars/25205

This is one of the research seminars for the RAS program, that distinguishes itself from the postdocs and program associates seminars in that speakers are chosen among Research Members, Research Professors with occasional outside speakers.

Video

Quasi-Morphisms On Surface Diffeomorphism Groups

Abstract/Media

To participate in this seminar, please register here: https://www.msri.org/seminars/25205

Abstract:

We will construct nontrivial quasimorphisms on the group of diffeomorphisms of a surface of genus at least 1 which are isotopic to the identity. This involves considering the graph whose vertices correspond to curves on the surface (not up to isotopy!), and transferring usual curve graph methods to this setting. In particular, we show that it is hyperbolic, and we construct elements of Diff_0(S) which act as independent enough hyperbolic elements on it. As a consequence, we also solve a question by Burago-Ivanov-Polterovich on the unboundedness of the fragmentation norm. This is joint work with Jonathan Bowden and Richard Webb. If time permits, I will also talk about work in progress that is additionally joint with Katie Mann and Emmanuel Militon, dynamically characterizing hyperbolic isometries of our curve graph of the torus.

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Quasi-Morphisms On Surface Diffeomorphism Groups

H.264 Video 25309_28867_8546_Quasi-Morphisms_on_Surface_Diffeomorphism_Groups.mp4