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Holomorphic disks and genus
bounds
Peter Ozsvath and Zoltan Szabo |
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Geometry & Topology 8 (2004) 311–334
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arXiv: math.GT/0311496 |
Abstract |
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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. This leads 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 element of Heegaard Floer homology associated to a weakly symplectically fillable contact structure is non-trivial. In particular, for certain three-manifolds, Heegaard Floer homology gives obstructions to the existence of taut foliations. |
Keywords
Thurston norm, Dehn surgery, Seifert genus, Floer homology,
contact structures
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Mathematical Subject Classification 2000
Primary: 57R58, 53D40
Secondary: 57M27, 57N10
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References |
Forward citations |
Publication
Received: 3 December 2003
Revised: 12 February 2004
Accepted: 14 February 2004
Published: 14 February 2004
Proposed: Robion Kirby
Seconded: John Morgan, Ronald Stern
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Authors |
| Peter Ozsvath | |
| Department of Mathematics Columbia University New York New York 10025 USA |
Institute for Advanced Study Princeton New Jersey 08540 USA |
| Zoltan Szabo | |
| Department of Mathematics Princeton University Princeton New Jersey 08544 USA |
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