Room P3.10, Mathematics Building

Luís Diogo, Stanford
Floer homology and holomorphic curves

Floer homology is a powerful tool in symplectic geometry. It is often hard to compute it explicitly, because it involves counting solutions of a perturbed Cauchy-Riemann equation. I will explain an approach to showing how Floer homology can instead be described (under certain hypotheses) by counting solutions of (unperturbed) Cauchy-Riemann equations, as well as gradient flow lines of auxiliary Morse functions. The advantage is that this information can sometimes be computed explicitly. This framework seems adequate for studying spectral invariants, symplectic homology and Floer-type operations. This is part of a joint project with S. Borman, Y. Eliashberg, S. Lisi and L. Polterovich.