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## Holomorphic disks and genus bounds

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Venue: | Geom. Topol |

Citations: | 28 - 8 self |

### Citations

393 |
Foliations and the topology of 3–manifolds
- Gabai
- 1983
(Show Context)
Citation Context ...) is diffeomorphic to S 3 p(U) (where here U is the unknot) under an orientationpreserving diffeomorphism, then K is the unknot. The first ingredient in the proof of Theorem 1.1 is a theorem of Gabai =-=[8]-=- which expresses the minimal genus problem in terms of taut foliations. This result, togetherHOLOMORPHIC DISKS AND GENUS BOUNDS 3 with a theorem of Eliashberg and Thurston [5] gives a reformulation i... |

274 | Holomorphic disks and topological invariants for closed threemanifolds, - Ozsvath, Szabo - 2004 |

237 | Floer homology and knot complements - Rasmussen - 2003 |

227 |
Stipsicz 4-manifolds and Kirby calculus,
- Gompf, A
- 1999
(Show Context)
Citation Context ... can be viewed as equivalence classes of nowhere vanishing vector fields over Y , where two vector fields are considered equivalent if they are homotopic in the complement of a ball in Y , c.f. [40], =-=[12]-=-. Dually, an oriented two-plane distribution gives rise to an equivalence class of nowhere vanishing vector fields (which are transverse to the distribution, and form a positive basis for TY ). Now, t... |

201 | Holomorphic disks and three-manifold invariants: properties and applications, - Ozsvath, Szabo - 2004 |

200 | Géométrie de contact: de la dimension trois vers les dimensions supérieures - Giroux - 2002 |

184 | Holomorphic disks and knot invariants - Ozsváth, Szabó |

183 | Absolutely graded Floer homologies and intersection forms for four-manifolds with boundary, - Ozsvath, Szabo - 2003 |

178 | Knots are determined by their complements - Gordon, Luecke - 1989 |

168 | A norm for the homology of 3–manifolds - Thurston - 1986 |

166 |
Convexité en topologie de contact
- Giroux
- 1991
(Show Context)
Citation Context ...etching the construction, we describe a refinement which lives in Floer homology with twisted coefficients. The contact invariant is constructed with the help of some work of Giroux. Specifically, in =-=[11]-=-, Giroux shows that contact structures over Y are in one-to-one correspondence with equivalence classes of open book decompositions of Y , under an equivalence relation given by a suitable notion of s... |

140 | On knot Floer homology and lens space surgeries, - Ozsvath, Szabo - 2005 |

135 | Heegaard Floer homologies and contact structures - Ozsváth, Szabó |

124 | Holomorphic triangles and invariants for smooth four-manifolds, - Ozsváth, Szabó - 2006 |

113 |
Lefschetz pencils on symplectic manifolds
- Donaldson
- 1999
(Show Context)
Citation Context ...ield-theoretic properties of Heegaard Floer homology, together with the suitable handle-decomposition of an arbitrary symplectic four-manifold induced from the Lefschetz pencils provided by Donaldson =-=[2]-=-. (The non-vanishing result from [32] is analogous to a non-vanishing theorem for the Seiberg-Witten invariants of symplectic manifolds proved by Taubes, c.f. [36] and [37].) 1.1. Contact structures. ... |

92 | Monopoles and contact structures. - Kronheimer, Mrowka - 1997 |

92 | Tight contact structures and Seiberg-Witten invariants - Lisca, Matić - 1997 |

85 | Heegaard Floer homology and alternating knots - Ozsváth, Szabó |

75 | Lefschetz fibrations on compact Stein surfaces
- Akbulut, Ozbagci
(Show Context)
Citation Context ...that ω extends smoothly over X = W ∪Y V . Although Eliashberg’s is the construction we need, concave fillings have been constructed previously in a number of different contexts, see for example [22], =-=[1]-=-, [7], [10], [25]. Indeed, since the first posting of the present article, Etnyre pointed out to us an alternate proof of Eliashberg’s theorem [6], see also [25]. In the construction, V is given as th... |

65 | A few remarks about symplectic filling
- Eliashberg
(Show Context)
Citation Context ...nd Thurston [5] gives a reformulation in terms of certain symplectically semi-fillable contact structures. The final breakthrough which makes this paper possible is an embedding theorem of Eliashberg =-=[3]-=-, see also [6] and [25], which shows that a symplectic semi-filling of a three-manifold can be embedded in a closed, symplectic four-manifold. From this, we then appeal to a theorem [32], which implie... |

59 |
Convex Symplectic Manifolds, Several complex variables and complex geometry, Part 2
- Eliashberg, Gromov
- 1989
(Show Context)
Citation Context ... boundary Y . A fourmanifold W is said to have convex boundary if there is a contact structure ξ over Y with the property that the restriction of ω to the two-planes of ξ is everywhere positive, c.f. =-=[3]-=-. Indeed, if we fix the contact structure Y over ξ, we say that W is a convex weak symplectic filling of (Y, ξ). If W is a convex weak symplectic filling of a possibly disconnected three-manifold Y ′ ... |

53 | A unique decomposition theorem for 3-manifolds - Milnor - 1962 |

52 | On Symplectic Cobordisms
- Etnyre, Honda
(Show Context)
Citation Context ...e (Y, ξ) admits a weak convex symplectic filling, it is called weakly fillable. Note that every contact structure (Y, ξ) can be realized as the concave boundary of some symplectic four-manifold (c.f. =-=[7]-=-, [10], and [3]). This is one justification for dropping the modifier “convex” from the terminology “weakly fillable”. If a contactHOLOMORPHIC DISKS AND GENUS BOUNDS 7 structure (Y, ξ) admits a weak ... |

52 | On the Ozsvath-Szabo invariant of negative definite plumbed 3-manifolds Geom. - Nemethi - 2005 |

50 | The Seiberg-Witten invariants and symplectic - Taubes - 1994 |

49 | Seiberg Witten and Gromov invariants for symplectic 4-manifolds, - Taubes - 2000 |

48 |
Foliations and the topology of 3-manifolds III
- Gabai
- 1987
(Show Context)
Citation Context ...result in turn leads to an alternate proof of a theorem proved jointly by Kronheimer, Mrowka, and us [19], first conjectured by Gordon [13] (the cases where p = 0 and ±1 follow from theorems of Gabai =-=[9]-=- and Gordon and Luecke [14] respectively): Corollary 1.3. [19] Let K ⊂ S 3 be a knot with the property that for some integer p, S 3 p(K) is diffeomorphic to S 3 p(U) (where here U is the unknot) under... |

46 | Holomorphic triangle invariants and the topology of symplectic four-manifolds - Ozsváth, Szabó - 2003 |

38 | Torsion invariants of Spinc -structures on 3-manifolds, - Turaev - 1997 |

35 |
Some aspects of classical knot theory
- Gordon
- 1977
(Show Context)
Citation Context ...the largest integer s for which the group ̂HFK∗(K, s) ̸= 0. This result in turn leads to an alternate proof of a theorem proved jointly by Kronheimer, Mrowka, and us [19], first conjectured by Gordon =-=[13]-=- (the cases where p = 0 and ±1 follow from theorems of Gabai [9] and Gordon and Luecke [14] respectively): Corollary 1.3. [19] Let K ⊂ S 3 be a knot with the property that for some integer p, S 3 p(K)... |

32 | Floer homology for Seiberg-Witten monopoles, in preparation - Kronheimer, Mrowka |

30 | Symplectic fillings and positive scalar curvature, Geometry & Topology 2 - Lisca - 1998 |

29 | Simple singularities and topology of symplectically filling 4-manifolds, - Ohta, Ono - 1999 |

28 | constrains on symplectic forms from the SeibergWitten invariants. - Taubes - 1995 |

26 | Scalar curvature and the Thurston norm, - Kronheimer, Mrowka - 1997 |

25 | Seifert fibered contact three–manifolds via surgery - Lisca, Stipsicz - 2004 |

19 | Explicit concave fillings of contact three-manifolds
- Gay
(Show Context)
Citation Context ... ξ) admits a weak convex symplectic filling, it is called weakly fillable. Note that every contact structure (Y, ξ) can be realized as the concave boundary of some symplectic four-manifold (c.f. [7], =-=[10]-=-, and [3]). This is one justification for dropping the modifier “convex” from the terminology “weakly fillable”. If a contactHOLOMORPHIC DISKS AND GENUS BOUNDS 7 structure (Y, ξ) admits a weak symple... |

19 | On symplectic fillings, Algebr - Etnyre |

16 | On symplectic fillings,
- Etnyre
- 2004
(Show Context)
Citation Context ...] gives a reformulation in terms of certain symplectically semi-fillable contact structures. The final breakthrough which makes this paper possible is an embedding theorem of Eliashberg [3], see also =-=[6]-=- and [25], which shows that a symplectic semi-filling of a three-manifold can be embedded in a closed, symplectic four-manifold. From this, we then appeal to a theorem [32], which implies the non-vani... |

7 | Convex symplectic manifolds, from: “Several complex variables and complex geometry, Part 2 - Eliashberg, Gromov - 1989 |

5 | 4-manifolds and Kirby calculus, volume 20 - Gompf, Stipsicz - 1999 |

3 | Some aspects of classical knot theory, from: “Knot theory - Gordon - 1978 |