QM Research Seminar: The Heegaard Floer - ECH isomorphism for sutured manifolds

Speaker: Paolo Ghiggini (Université Grenoble Alpes)

Abstract:

Vincent Colin, Ko Honda, Michael Hutchings and I defined embedded contact homology groups for sutured three-manifolds as a slight modification of Hutching's embedded contact homology for closed three manifolds. I will sketch a strategy to prove that those groups are isomorphic to Juhász's sutured Floer homology, and therefore are topological invariants. The strategy is to extend the knot complement to a larger closed manifold, and then apply the isomorphism between Heegaard Floer homology and embedded contact homology to the closed manifold. In the talk I will focus on the effect of that extension on embedded contact homology, and therefore no knowledge of suitured Floer homology will be necessary beyond the fact that it exists and is interesting. On the other hand the definition of embedded contact homology for sutured three-manifolds will be sketched. This is a joint work in progress with Vincent Colin and Ko Honda.