Quasimorphisms on diffeomorphism groups

Abstract: I will explain how to construct an unbounded quasimorphism on the group of isotopically-trivial diffeomorphisms of a surface of positive genus. As a corollary the commutator length and fragmentation norm are both (stably) unbounded, which solves a problem of Burago--Ivanov--Polterovich. The proof uses a new hyperbolic graph on which these groups act by isometries, which is inspired by techniques from mapping class groups. This is joint work with Jonathan Bowden and Sebastian Hensel.

Mathematics

Audience: researchers in the topic

Regensburg low-dimensional geometry and topology seminar