Holomorphic discs and surgery exact triangles

Abstract

We show a connection between a surgery exact sequence in knot Floer homology and the sequence derived in [18]. As a consequence of this relationship we see that the exact sequence in [18] also works with coherent orientations and admits refinements with respect to spinc-structures. As an application of this discussion, we prove that the ranks of the image and kernel of certain cobordism maps between knot Floer homologies can be computed combinatorially by relating them to a count of certain moduli spaces of holomorphic disks.