On symplectic fillings

Etnyre, John B

doi:10.2140/agt.2004.4.73

Etnyre, John B ¹

¹Department of Mathematics, University of Pennsylvania, 209 South 33rd St, Philadelphia PA 19104-6395, USA

Algebraic and Geometric Topology, Tome 4 (2004) no. 1, pp. 73-80

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Résumé

In this note we make several observations concerning symplectic fillings. In particular we show that a (strongly or weakly) semi-fillable contact structure is fillable and any filling embeds as a symplectic domain in a closed symplectic manifold. We also relate properties of the open book decomposition of a contact manifold to its possible fillings. These results are also useful in proving property P for knots [P Kronheimer and T Mrowka, Geometry and Topology, 8 (2004) 295–310] and in showing the contact Heegaard Floer invariant of a fillable contact structure does not vanish [P Ozsvath and Z Szabo, Geometry and Topology, 8 (2004) 311–334].

DOI : 10.2140/agt.2004.4.73

Keywords: tight, symplectic filling, convexity

Affiliations des auteurs :

Etnyre, John B ¹

¹ Department of Mathematics, University of Pennsylvania, 209 South 33rd St, Philadelphia PA 19104-6395, USA

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Etnyre, John B. On symplectic fillings. Algebraic and Geometric Topology, Tome 4 (2004) no. 1, pp. 73-80. doi: 10.2140/agt.2004.4.73

Bibliographie
Cité par

[1] S Akbulut, B Ozbagci, On the topology of compact Stein surfaces, Int. Math. Res. Not. (2002) 769

[2] F Ding, H Geiges, Symplectic fillability of tight contact structures on torus bundles, Algebr. Geom. Topol. 1 (2001) 153

[3] Y Eliashberg, A few remarks about symplectic filling, Geom. Topol. 8 (2004) 277

[4] Y Eliashberg, Unique holomorphically fillable contact structure on the 3–torus, Internat. Math. Res. Notices (1996) 77

[5] Y Eliashberg, Contact 3–manifolds twenty years since J. Martinet's work, Ann. Inst. Fourier (Grenoble) 42 (1992) 165

[6] Y Eliashberg, On symplectic manifolds with some contact properties, J. Differential Geom. 33 (1991) 233

[7] Y Eliashberg, Topological characterization of Stein manifolds of dimension $>2$, Internat. J. Math. 1 (1990) 29

[8] Y Eliashberg, Filling by holomorphic discs and its applications, from: "Geometry of low-dimensional manifolds, 2 (Durham, 1989)", London Math. Soc. Lecture Note Ser. 151, Cambridge Univ. Press (1990) 45

[9] Y M Eliashberg, W P Thurston, Confoliations, University Lecture Series 13, American Mathematical Society (1998)

[10] J B Etnyre, Symplectic convexity in low-dimensional topology, Topology Appl. 88 (1998) 3

[11] J B Etnyre, K Honda, On symplectic cobordisms, Math. Ann. 323 (2002) 31

[12] J B Etnyre, K Honda, Tight contact structures with no symplectic fillings, Invent. Math. 148 (2002) 609

[13] D T Gay, Explicit concave fillings of contact three-manifolds, Math. Proc. Cambridge Philos. Soc. 133 (2002) 431

[14] 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

[15] R E Gompf, Handlebody construction of Stein surfaces, Ann. of Math. $(2)$ 148 (1998) 619

[16] N Goodman, Contact structures and open books, PhD thesis, University of Texas at Austin (2003)

[17] M Gromov, Pseudoholomorphic curves in symplectic manifolds, Invent. Math. 82 (1985) 307

[18] P B Kronheimer, T S Mrowka, Witten's conjecture and property P, Geom. Topol. 8 (2004) 295

[19] P B Kronheimer, T S Mrowka, Monopoles and contact structures, Invent. Math. 130 (1997) 209

[20] P Kronheimer, T Mrowka, P Ozsváth, Z Szabó, Monopoles and lens space surgeries, Ann. of Math. $(2)$ 165 (2007) 457

[21] P Lisca, Symplectic fillings and positive scalar curvature, Geom. Topol. 2 (1998) 103

[22] P Lisca, On symplectic fillings of 3–manifolds, from: "Proceedings of 6th Gökova Geometry–Topology Conference" (1999) 151

[23] P Lisca, G Matić, Tight contact structures and Seiberg–Witten invariants, Invent. Math. 129 (1997) 509

[24] P Lisca, A I Stipsicz, An infinite family of tight, not semi-fillable contact three-manifolds, Geom. Topol. 7 (2003) 1055

[25] D Mcduff, Symplectic manifolds with contact type boundaries, Invent. Math. 103 (1991) 651

[26] D Mcduff, The structure of rational and ruled symplectic 4–manifolds, J. Amer. Math. Soc. 3 (1990) 679

[27] H Ohta, K Ono, Simple singularities and topology of symplectically filling 4–manifold, Comment. Math. Helv. 74 (1999) 575

[28] P Ozsváth, Z Szabó, Holomorphic disks and genus bounds, Geom. Topol. 8 (2004) 311

[29] A I Stipsicz, On the geography of Stein fillings of certain 3–manifolds, Michigan Math. J. 51 (2003) 327

[30] W P Thurston, H E Winkelnkemper, On the existence of contact forms, Proc. Amer. Math. Soc. 52 (1975) 345

[31] A Weinstein, Contact surgery and symplectic handlebodies, Hokkaido Math. J. 20 (1991) 241

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