I will discuss a recent work constructing quasimorphisms on the group of area and orientation preserving homeomorphisms of the two-sphere. The existence of these quasimorphisms answers a question of Entov, Polterovich, and Py. As an immediate corollary, we learn that the commutator length is unbounded, sharply contrasting a result of Tsuboi regarding the group of homeomorphisms that do not preserve area. A key role is played by ‘link spectral invariants’, constructed using a kind of quantitative variant of the Heegaard Floer cohomology for links.
This is joint work with Humilière, Mak, Seyfaddini, and Smith.
This video is part of the Institute for Advanced Study‘s Symplectic geometry seminar.
