Lagrangian link quasimorphisms and the non-simplicity of Hameomorphism group of surfaces

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• Cheuk Yu Mak (Southampton)
• Wednesday 01 November 2023, 16:00-17:00
• MR13.

If you have a question about this talk, please contact Oscar Randal-Williams.

In this talk, we will explain the construction of a sequence of homogeneous quasi-morphisms of the area-preserving homeomorphism group of the sphere using Lagrangian Floer theory for links. The first-order information of this sequence enables us to show that the area-preserving homeomorphism group is not simple, with the Hameomorphism group being a non-trivial proper normal subgroup. The second-order information allows us to show that the Hameomorphism group is not simple either. If time permits, we will explain how to generalize it to all positive genus surfaces even though we no longer have quasi-morphisms.

The case of the sphere is joint work with Daniel Cristofaro-Gardiner, Vincent Humilière, Sobhan Seyfaddini, and Ivan Smith. The case of positive genus surfaces is joint work with Ibrahim Trifa.

This talk is part of the Differential Geometry and Topology Seminar series.

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