The Quasimorphism Question - Daniel Anthony
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.