Gauge theory and Stein fillings of certain 3-manifolds

Turkish Journal of Mathematics

Volumn 26, Issue 1, 2002, Pages 115-130

  Stipsicz, András I ^a,b  

^a EÖTVÖS LORÁND UNIVERSITY   (Hungary)

^b PRINCETON UNIVERSITY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0242673519     PISSN: 13000098     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article

References (39)

1. B. Aebisher et al., Symplectic geometry, Progress Math. 124, Birkhäuser, Boston, MA, 1994.
2. S. Akbulut and B. Ozbagci, Lefschetz fibrations on compact Stein surfaces, Geometry and Topology, 5 (2001), 319-334.
3. S. Akbulut and B. Ozbagci, On the topology of compact Stein surfaces, preprint (arXiv:math.GT/0103106).
4. F. Ding and H. Geiges Symplectic fillability of tight contact structures on torus bundles Alg. and Geom. Topology, 1 (2001), 153-172.
5. S. Donaldson and P. Kronheimer, Geometry of 4-manifolds, Oxford Univ. Press, 1990.
6. Y. Eliashberg, Filling by holomorphic disks and its applications, Geometry of Low-Dimensional Manifolds: 2, Proc. Durham Symp. 1989, London Math. Soc. Lecture Notes, 151, Cambridge Univ. Press, 1990, 45-67.
7. Y. Eliashberg, Topological characterization of Stein manifolds of dimension > 2, Internat. J. of Math. 1 (1990), 29-46.
8. Y. Eliashberg, Unique holomorphically fillable contact structure on the 3-torus, Internat. Math. Res. Notices (1996), 77-82.
9. Y. Eliashberg, Symplectic topology in the nineties, Diff. Geom. and its Appl. 9 (1998), 59-88.
10. J. Etnyre and K. Honda, On the nonexistence of tight structures, Ann. Math. 153 (2001), 749-766.
11. R. Fintushel and R. Stern, Knots, links and 4-manifolds, Invent. Math. 134 (1998), 363-400.
12. M. Freedman and F. Quinn, Topology of 4-manifolds, Princeton Mathematical Series 39, Princeton University Press, 1990.
13. K. Frøyshov, The Seiberg-Witten equations and four-manifolds with boundary, Math. Res. Lett. 3 (1996), 373-390.
14. M. Furuta, Monopole equation and the 11/8-conjecture, Math. Res. Lett. 8 (2001), 279-291.
15. P. Ghiggini and S. Schönenberger, On the classification of tight contact structures, preprint (arXiv:math.GT/0201099).
16. E. Giroux, Une structure de contact, meme tendue est plus ou moins tordue, Ann. Scient. Ecole Normale Sup. 27 (1994), 697-705.
17. R. Gompf, Handlebody construction of Stein surfaces, Ann. of Math. 148 (1998), 619-693.
18. R. Gompf and A. Stipsicz, 4-manifolds and Kirby calculus, Grad. Stud. in Math. AMS, 1999.
19. H. Grauert, On Levi's problem, Ann. Math. 68 (1958), 460-472.
20. K. Honda, personal communication.
21. Y. Kanda, The classification of tight contact structures on the 3-torus, Comm. Anal. and Geom., 5 (1997), 413-438.
22. P. Lisca, Symplectic fillings and positive scalar curvature, Geom. Topol. 2 (1998), 103-116.
23. P. Lisca, On symplectic fillings of 3-manifolds, Proc. of Gökova Geometry and Topology Conference (1998), 151-160.
24. P. Lisca and G. Matić, Tight contact structures and Seiberg-Witten invariants, Invent. Math. 129 (1997), 509-525.
25. 4, Invent. Math. 143 (2001), 325-348.
26. D. McDuff, The structure of rational and ruled symplectic 4-manifolds Journal of the Amer. Math. Soc. 3 (1990), 679-712.
27. J. Milnor, Morse theory, Ann. Math. Studies 51, Princeton University Press, 1963.
28. J. Morgan, The Seiberg- Witten equations and applications to the topology of smooth four-manifolds, Math. Notes 44, Princeton University Press, Princeton NJ, 1996.
29. J. Morgan and Z. Szabó, Homotopy K3-surfaces and mod 2 Seiberg-Witten invariants, Math. Res. Lett. 4 (1997), 17-21.
30. T. Mrowka, P. Ozsváth and B. Yu, Seiberg- Witten monopoles on Seifert fibered spaces, Comm. Anal. Geom. 5 (1997), 685-791.
31. H. Ohta and K. Ono, Simple singularities and topology of symplectically filling 4-manifold, Comment. Math. Helv. 74 (1999), 575-590.
32. P. Ozsváth and Z. Szabó, The symplectic Thom conjecture, Annals of Math. 152 (2000), 93-124.
33. P. Ozsváth and Z. Szabó, On embedding of circle bundles in 4-manifolds, Math. Res. Letters 7 (2000), 657-669.
34. V. Rohlin, A three-dimensional manifold is the boundary of a four-dimensional one, Dokl. Akad. Nauk SSSR 81 (1951), 355-357.
35. A. Stipsicz and Z. Szabó, Gluing 4-manifolds along ∑(2,3,11), Top. and its Applications, 106 (2000), 293-304.
36. C. Taubes, The Seiberg- Witten invariants and 4-manifolds with essential tori, Geometry and Topology 5 (2001), 441-519.
37. P. Teichner, Topological four-manifolds with finite fundamental group PhD Thesis, University of Mainz, Germany, 1992.
38. C. T. C. Wall, Surgery on compact manifolds, LMS Monographs, Academic Press, 1970.
39. E. Witten, Monopoles and four-manifolds, Math. Res. Lett. 1 (1994), 769-796.