Holomorphic discs and surgery exact triangles
arXiv:1002.4141
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.
30 pages, 13 figures; Reorganized paper and exposition, added a detailed introduction and details to several proofs; corrected references; Both §6 and §7 taken out