Area-preserving homeomorphisms and link spectral invariants

Appears in collection : Giroux 60 - Convexity in contact and symplectic topology

We will discuss various results concerning the algebraic structure of the group of area-preserving homeomorphisms of a compact surface. The results are obtained from the asymptotics of spectral invariants associated to configurations of disjoint circles on the surface. These link spectral invariants are in turn defined from the Floer cohomology of an associated Lagrangian in the symmetric product. This talk reports on joint work with Dan Cristofaro-Gardiner, Vincent Humilière, Cheuk-Yu Mak and Sobhan Seyfaddini.