Holomorphic disks and genus bounds

• DOI: 10.2140/gt.2004.8.311
• Publication Date: 2005-06-15T12:10:25Z
• Authors: Peter Ozsvath; Zoltan Szabo
• Keywords: Floer Homology; Morse homology; Homology; Khovanov homology

We prove that, like the Seiberg-Witten monopole homology, Heegaard Floer homology for a three-manifold determines its Thurston norm.As consequence, we show that knot detects genus of knot.This leads to new proofs certain results previously obtained using (in collaboration with Kronheimer and Mrowka).It also purely Morse-theoretic interpretation knot.The method proof shows canonical element associated weakly symplectically fillable contact structure is non-trivial.In particular, three-manifolds, gives obstructions existence taut foliations.