Holomorphic disks and genus bounds

  title={Holomorphic disks and genus bounds},
  author={Peter S. Ozsvath and Zolt{\'a}n Imre Szab{\'o}},
  journal={Geometry \& Topology},
We prove that, like the Seiberg-Witten monopole homology, the Heegaard Floer homology for a three-manifold determines its Thurston norm. As a consequence, we show that knot Floer homology detects the genus of a knot. Thisleads to new proofs of certain results previously obtained using Seiberg-Witten monopole Floer homology (in collaboration with Kronheimer and Mrowka). It also leads to a purely Morse-theoretic interpretation of the genus of a knot. The method of proof shows that the canonical… Expand
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