Cobordism maps in link Floer homology
Cobordism maps in link Floer homology

Marco Marengon , Imperial College London
Fine Hall 314
Given a (decorated) link cobordism between two links K and L (that is, an embedded surface in S^3 x [0,1] that K and L cobound), Juhász defined a map between their link Floer homologies. We prove that when the surface is an annulus the map preserves the natural bigrading of HFL and is always nonzero. This has some interesting applications, in particular the existence of a nonzero element in HFL(K) associated to each properly embedded disc in B^4 whose boundary is the knot K in S^3. I will then discuss some properties of the map in HFL when the cobordism is not necessarily given by an annulus. This is joint work with András Juhász.