English

Holomorphic discs and surgery exact triangles

Geometric Topology 2011-02-22 v2

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.

Keywords

Cite

@article{arxiv.1002.4141,
  title  = {Holomorphic discs and surgery exact triangles},
  author = {Bijan Sahamie},
  journal= {arXiv preprint arXiv:1002.4141},
  year   = {2011}
}

Comments

30 pages, 13 figures; Reorganized paper and exposition, added a detailed introduction and details to several proofs; corrected references; Both {\S}6 and {\S}7 taken out

R2 v1 2026-06-21T14:49:48.881Z