Université libre de Bruxelles, 23/01/2017
“Cobordism maps in knot Floer homology”
Decorated knot cobordisms functorially induce maps on knot Floer homology. We compute these maps for elementary cobordisms, and hence give a formula for the Alexander and Maslov grading shifts. We also show a non-vanishing result in the case of concordances and present some applications to invertible concordances. This is joint work with Marco Marengon.
“Loops and L-spaces”
An L-space is a closed oriented 3-manifold whose Heegaard Floer homology is as simple as possible. A surpising conjecture of Boyer-Gordon-Watson says that a prime 3-manifold Y is an L-space if and only if pi_1(Y) is non-left orderable. The conjecture suggest some strong statements about when a manifold containing an incompressible torus is an L-space.
I’ll give a geometrical proof of these statements by viewing the Heegaard Floer homology of a manifold with torus boundary as an element of the Fukaya category of the punctured torus. As a consequece the BGW conjecture holds for graph manifolds. This is joint work with Jonathan Hanselman and Liam Watson.
“Filtering the Heegaard Floer contact invariant”
The modern development of contact geometry in 3 dimensions has seen several (due to Giroux, Wendl, Latschev and Wendl, Hutchings, and others) invariants of contact structures meant in some sense to measure non-(Stein/symplectic)-fillability of the structure. We will discuss a new approach which uses Heegaard Floer homology to define an invariant with a similar aim, but which has several desirable properties lacking in earlier approaches. Time permitting, we will discuss some examples and applications. This is joint with joint work with Kutluhan, Matic, and Van Horn-Morris.