Holomorphic discs and surgery exact triangles

Details Holomorphic discs and surgery exact triangles Holomorphic discs and surgery exact triangles

2010-02-22

arxiv.org/abs/1002.4141v2

Mathematics

Geometric Topology

30 pages, 13 figures; Reorganized paper and exposition, added a detailed introduction and details to several proofs; corrected

Scientific paper

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.

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