Holomorphic disks and knot invariants

@article{Ozsvath2002HolomorphicDA,
  title={Holomorphic disks and knot invariants},
  author={Peter S. Ozsvath and Zolt{\'a}n Imre Szab{\'o}},
  journal={Advances in Mathematics},
  year={2002},
  volume={186},
  pages={58-116}
}
Abstract We define a Floer-homology invariant for knots in an oriented three-manifold, closely related to the Heegaard Floer homologies for three-manifolds defined in an earlier paper. We set up basic properties of these invariants, including an Euler characteristic calculation, and a description of the behavior under connected sums. Then, we establish a relationship with HF + for surgeries along the knot. Applications include calculation of HF + of three-manifolds obtained by surgeries on some… Expand
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In an earlier paper, we introduced a knot invariant for a null-homologous knot K in an oriented three-manifold Y , which is closely related to the Heegaard Floer homology of Y . In this paper weExpand
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We use the Ozsvath-Szabo theory of Floer homology to define an invariant of knot complements in three-manifolds. This invariant takes the form of a filtered chain complex, which we call CF_r. ItExpand
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