#### Volume 8, issue 1 (2004)

 Download this article For screen For printing
 Recent Issues
 The Journal About the Journal Subscriptions Editorial Board Editorial Interests Editorial Procedure Submission Guidelines Submission Page Ethics Statement Author Index To Appear ISSN (electronic): 1364-0380 ISSN (print): 1465-3060 Other MSP Journals
Holomorphic disks and genus bounds

### Peter Ozsvath and Zoltan Szabo

Geometry & Topology 8 (2004) 311–334
##### Bibliography
 1 S Akbulut, B Ozbagci, Lefschetz fibrations on compact Stein surfaces, Geom. Topol. 5 (2001) 319 MR1825664 2 S K Donaldson, Lefschetz pencils on symplectic manifolds, J. Differential Geom. 53 (1999) 205 MR1802722 3 Y Eliashberg, A few remarks about symplectic filling, Geom. Topol. 8 (2004) 277 MR2023279 4 Y Eliashberg, M Gromov, Convex symplectic manifolds, from: "Several complex variables and complex geometry, Part 2 (Santa Cruz, CA, 1989)", Proc. Sympos. Pure Math. 52, Amer. Math. Soc. (1991) 135 MR1128541 5 Y M Eliashberg, W P Thurston, Confoliations, University Lecture Series 13, American Mathematical Society (1998) MR1483314 6 J B Etnyre, On symplectic fillings, Algebr. Geom. Topol. 4 (2004) 73 MR2023278 7 J B Etnyre, K Honda, On symplectic cobordisms, Math. Ann. 323 (2002) 31 MR1906906 8 D Gabai, Foliations and the topology of 3–manifolds, J. Differential Geom. 18 (1983) 445 MR723813 9 D Gabai, Foliations and the topology of 3–manifolds III, J. Differential Geom. 26 (1987) 479 MR910018 10 D T Gay, Explicit concave fillings of contact three-manifolds, Math. Proc. Cambridge Philos. Soc. 133 (2002) 431 MR1919715 11 E Giroux, Géométrie de contact: de la dimension trois vers les dimensions supérieures, from: "Proceedings of the International Congress of Mathematicians, Vol II (Beijing, 2002)", Higher Ed. Press (2002) 405 MR1957051 12 R E Gompf, A I Stipsicz, 4–manifolds and Kirby calculus, Graduate Studies in Mathematics 20, American Mathematical Society (1999) MR1707327 13 C M Gordon, Some aspects of classical knot theory, from: "Knot theory (Proc. Sem., Plans-sur–Bex, 1977)", Lecture Notes in Math. 685, Springer (1978) 1 MR521730 14 C M Gordon, J Luecke, Knots are determined by their complements, J. Amer. Math. Soc. 2 (1989) 371 MR965210 15 L H Kauffman, On knots, Annals of Mathematics Studies 115, Princeton University Press (1987) MR907872 16 P B Kronheimer, T S Mrowka, Floer homology for Seiberg–Witten Monopoles, in preparation 17 P B Kronheimer, T S Mrowka, Monopoles and contact structures, Invent. Math. 130 (1997) 209 MR1474156 18 P B Kronheimer, T S Mrowka, Scalar curvature and the Thurston norm, Math. Res. Lett. 4 (1997) 931 MR1492131 19 P Kronheimer, T Mrowka, P Ozsváth, Z Szabó, Monopoles and lens space surgeries, Ann. of Math. $(2)$ 165 (2007) 457 MR2299739 20 P Lisca, Symplectic fillings and positive scalar curvature, Geom. Topol. 2 (1998) 103 MR1633282 21 P Lisca, A I Stipsicz, Seifert fibered contact three-manifolds via surgery, Algebr. Geom. Topol. 4 (2004) 199 MR2059189 22 P Lisca, G Matić, Tight contact structures and Seiberg–Witten invariants, Invent. Math. 129 (1997) 509 MR1465333 23 J Milnor, A unique decomposition theorem for 3–manifolds, Amer. J. Math. 84 (1962) 1 MR0142125 24 A Némethi, On the Ozsváth–Szabó invariant of negative definite plumbed 3–manifolds, Geom. Topol. 9 (2005) 991 MR2140997 25 H Ohta, K Ono, Simple singularities and topology of symplectically filling 4–manifold, Comment. Math. Helv. 74 (1999) 575 MR1730658 26 P Ozsváth, Z Szabó, Holomorphic disks and three-manifold invariants: properties and applications, Ann. of Math. $(2)$ 159 (2004) 1159 MR2113020 27 P Ozsváth, Z Szabó, Holomorphic disks and topological invariants for closed three-manifolds, Ann. of Math. $(2)$ 159 (2004) 1027 MR2113019 28 P Ozsváth, Z Szabó, Holomorphic triangles and invariants for smooth four-manifolds, Adv. Math. 202 (2006) 326 MR2222356 29 P Ozsváth, Z Szabó, On knot Floer homology and lens space surgeries, Topology 44 (2005) 1281 MR2168576 30 P Ozsváth, Z Szabó, Heegaard Floer homology and contact structures, Duke Math. J. 129 (2005) 39 MR2153455 31 P Ozsváth, Z Szabó, Holomorphic disks and knot invariants, Adv. Math. 186 (2004) 58 MR2065507 32 P Ozsváth, Z Szabó, Absolutely graded Floer homologies and intersection forms for four-manifolds with boundary, Adv. Math. 173 (2003) 179 MR1957829 33 P Ozsváth, Z Szabó, Heegaard Floer homology and alternating knots, Geom. Topol. 7 (2003) 225 MR1988285 34 P Ozsváth, Z Szabó, Holomorphic triangle invariants and the topology of symplectic four-manifolds, Duke Math. J. 121 (2004) 1 MR2031164 35 J Rasmussen, Floer homology and knot complements, PhD thesis, Harvard University (2003) 36 C H Taubes, The Seiberg–Witten invariants and symplectic forms, Math. Res. Lett. 1 (1994) 809 MR1306023 37 C H Taubes, More constraints on symplectic forms from Seiberg–Witten invariants, Math. Res. Lett. 2 (1995) 9 MR1312973 38 C H Taubes, Seiberg Witten and Gromov invariants for symplectic 4–manifolds, First International Press Lecture Series 2, International Press (2000) MR1798809 39 W P Thurston, A norm for the homology of 3–manifolds, Mem. Amer. Math. Soc. 59 (1986) MR823443 40 V Turaev, Torsion invariants of $\mathrm{Spin}^c$–structures on 3–manifolds, Math. Res. Lett. 4 (1997) 679 MR1484699 41 E Witten, Monopoles and four-manifolds, Math. Res. Lett. 1 (1994) 769 MR1306021