Admissible Dehn surgeries in tight contact manifolds

Vincent Colin[1]

  • [1] Université de Nantes, Département de Mathématiques, 2 rue de la Houssinière, 44322 Nantes Cedex 2 (France)

Annales de l’institut Fourier (2001)

  • Volume: 51, Issue: 5, page 1419-1435
  • ISSN: 0373-0956

Abstract

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We describe an example of a universally tight contact manifold that becomes overtwisted after an admissible Dehn surgery along a transverse link.

How to cite

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Colin, Vincent. "Chirurgies de Dehn admissibles dans les variétés de contact tendues." Annales de l’institut Fourier 51.5 (2001): 1419-1435. <http://eudml.org/doc/115953>.

@article{Colin2001,
abstract = {On décrit un exemple de variété de contact universellement tendue qui devient vrillée après une chirurgie de Dehn admissible sur un entrelacs transverse.},
affiliation = {Université de Nantes, Département de Mathématiques, 2 rue de la Houssinière, 44322 Nantes Cedex 2 (France)},
author = {Colin, Vincent},
journal = {Annales de l’institut Fourier},
keywords = {tight contact structure; Dehn surgery; symplectic filling},
language = {fre},
number = {5},
pages = {1419-1435},
publisher = {Association des Annales de l'Institut Fourier},
title = {Chirurgies de Dehn admissibles dans les variétés de contact tendues},
url = {http://eudml.org/doc/115953},
volume = {51},
year = {2001},
}

TY - JOUR
AU - Colin, Vincent
TI - Chirurgies de Dehn admissibles dans les variétés de contact tendues
JO - Annales de l’institut Fourier
PY - 2001
PB - Association des Annales de l'Institut Fourier
VL - 51
IS - 5
SP - 1419
EP - 1435
AB - On décrit un exemple de variété de contact universellement tendue qui devient vrillée après une chirurgie de Dehn admissible sur un entrelacs transverse.
LA - fre
KW - tight contact structure; Dehn surgery; symplectic filling
UR - http://eudml.org/doc/115953
ER -

References

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  1. V. Colin, Chirurgies d'indice 1 et isotopies de sphères dans les variétés de contact tendues, C. R. Acad. Sci. Paris, série 1 324 (1997), 659-663 Zbl0876.57051MR1447038
  2. V. Colin, Recollement de variétés de contact tendues, Bull. Soc. Math. France 127 (1999), 101-127 Zbl0930.53053MR1700468
  3. Y. Eliashberg, Filling by holomorphic discs and its applications, London Math. Soc. Lect. Notes Ser. 151 (1991), 45-67 Zbl0731.53036MR1171908
  4. Y. Eliashberg, Contact 3-manifolds, twenty years since Jean Martinet's work, Ann. Inst. Fourier 42 (1992), 165-192 Zbl0756.53017MR1162559
  5. Y. Eliashberg, Legendrian and transversal knots in tight contact manifolds, Topological methods in Modern Mathematics, (1993), Publish or Perish Zbl0809.53033MR1215964
  6. Y. Eliashberg, W. Thurston, Confoliations, Univ. Lect. Ser. vol. 13 (1998) Zbl0893.53001MR1483314
  7. D. Gay, Symplectic 4-dimensional 2-handles and contact surgery along transverse knots, (1999) 
  8. E. Giroux, Convexité en topologie de contact, Comment. Math. Helvetici 66 (1991), 18-33 Zbl0766.53028MR1129802
  9. E. Giroux, Topologie de contact en dimension 3, Sém. Bourbaki 760 (1992-1993), 1-27 
  10. S. Makar-Limanov, Tight contact structures on solid tori, Trans. Amer. Math. Soc. 350 (1998), 1013-1044 Zbl0894.53036MR1401526
  11. S. Schwartzmann, Asymptotic cycles, Ann. of Math. 66 (1957), 270-284 Zbl0207.22603MR88720

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