A Local Quasimorphism Property for Link Spectral Invariants

Given a finite collection of disjoint Lagrangian circles on a symplectic surface satisfying some area constraints, Cristofaro-Gardiner, Humilière, Mak, Seyfaddini and Smith define a link spectral invariant, by computing the Lagrangian Floer homology of the product of the circles inside the symmetric product of the surface. When the surface is the sphere, this spectral invariant is a quasimorphism, however this is not the case for higher genus surfaces. In this talk, I will show that the link spectral invariants on higher genus surfaces are local quasimorphisms, i.e. that their restriction to Hamiltonian diffeomorphisms supported in any given topological disc inside the surface is a quasimorphism. This is a joint work with Cheuk Yu Mak.