Knot Floer homology detects genus-one fibred knots

American Journal of Mathematics

Volumn 130, Issue 5, 2008, Pages 1151-1169

  Ghiggini, Paolo ^a  

^a UNIVERSITÉ DU QUÉBEC À MONTRÉAL   (Canada)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 54349104239     PISSN: 00029327     EISSN: None     Source Type: Journal    
DOI: 10.1353/ajm.0.0016     Document Type: Article

References (25)

1. A. Candel and L. Conlon, Foliations. I, Grad. Stud. Math., vol. 23, American Mathematical Society, Providence, RI, 2000.
2. F. Ding and H. Geiges, Symplectic fillability of tight contact structures on torus bundles, Algebr. Geom. Topol. 1 (2001), 153-172.
3. _, A Legendrian surgery presentation of contact 3-manifolds, Math. Proc. Cambridge Philos. Soc. 136 (3) (2004), 583-598.
4. Y. Eliashberg, A few remarks about symplectic filling, Geom. Topol. 8 (2004), 277-293.
5. Y. Eliashberg and W. Thurston, Confoliations, University Lecture Series, vol. 13, American Mathematical Society, Providence, RI, 1998.
6. D. Gabai, Foliations and the topology of 3-manifolds, J. Differential Geom. 18 (3) (1983), 445-503.
7. _, The Murasugi sum is a natural geometric operation, Low-Dimensional Topology (San Francisco, Calif., 1981), Contemp. Math., vol. 20, Amer. Math. Soc., Providence, RI, 1983, pp. 131-143.
8. _, Foliations and the topology of 3-manifolds. II, J. Differential Geom. 26 (3) (1987), 461-478.
9. _, Foliations and the topology of 3-manifolds. III, J. Differential Geom. 26 (3) (1987), 479-536.
10. P. Kronheimer, T. Mrowka, P. Ozsváth, and Z. Szabó, Monopoles and lens space surgeries, Ann. of Math. (2) 165 (2) (2007), 457-546.
11. P. Lisca and A. Stipsicz, Seifert fibered contact three-manifolds via surgery, Algebr. Geom. Topol. 4 (2004), 199-217.
12. Y. Ni, Knot Floer homology detects fibred knots, Invent. Math. 170 (3) (2007), 577-608.
13. P. Ozsváth and Z. Szabó, Heegaard Floer homology and alternating knots, Geom. Topol. 7 (2003), 225-254.
14. _, Holomorphic disks and genus bounds, Geom. Topol. 8 (2004), 311-334.
15. _, Holomorphic disks and knot invariants, Adv. Math. 186 (1) (2004), 58-116.
16. _, Holomorphic disks and three-manifold invariants: properties and applications, Ann. of Math. (2) 159 (3) (2004), 1159-1245.
17. _, Holomorphic disks and topological invariants for closed three-manifolds, Ann. of Math. (2) 159 (3) (2004), 1027-1158.
18. _, Holomorphic triangle invariants and the topology of symplectic four-manifolds, Duke Math. J. 121 (1) (2004), 1-34.
19. _, On Heegaard Floer homology and Seifert fibered surgeries, Proceedings of the Casson Fest, Geom. Topol. Monogr., vol. 7, Geom. Topol. Publ., Coventry, 2004, pp. 181-203.
20. _, Heegaard Floer homology and contact structures, Duke Math. J. 129 (1) (2005), 39-61.
21. _, Holomorphic triangles and invariants for smooth four-manifolds, Adv. Math. 202 (2) (2006), 326-400.
22. _, The Dehn surgery characterization of the trefoil and the figure eight knot, preprint available at ArXiv:math.GT/0604079.
23. J. Rasmussen, Floer homology and knot complements, Ph.D. thesis, Harvard University, ArXiv:math.GT/0306378.
24. D. Rolfsen, Knots and Links, Mathematics Lecture Series, vol. 7, Publish or Perish Inc., Houston, TX, 1990. Corrected reprint of the 1976 original.
25. 3, Trans. Amer. Math. Soc. 339 (2) (1993), 643-657.