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Open books on contact five-manifolds

Otto van Koert[1]

  • [1] Université Libre de Bruxelles Département de Mathématiques - CP 218 Boulevard du Triomphe 1050 Bruxelles (Belgique)

Annales de l’institut Fourier (2008)

  • Volume: 58, Issue: 1, page 139-157
  • ISSN: 0373-0956

Abstract

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By using open book techniques we give an alternative proof of a theorem about the existence of contact structures on five-manifolds due to Geiges. The theorem asserts that simply-connected five-manifolds admit a contact structure in every homotopy class of almost contact structures.

How to cite

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van Koert, Otto. "Open books on contact five-manifolds." Annales de l’institut Fourier 58.1 (2008): 139-157. <http://eudml.org/doc/10307>.

@article{vanKoert2008,
abstract = {By using open book techniques we give an alternative proof of a theorem about the existence of contact structures on five-manifolds due to Geiges. The theorem asserts that simply-connected five-manifolds admit a contact structure in every homotopy class of almost contact structures.},
affiliation = {Université Libre de Bruxelles Département de Mathématiques - CP 218 Boulevard du Triomphe 1050 Bruxelles (Belgique)},
author = {van Koert, Otto},
journal = {Annales de l’institut Fourier},
keywords = {Contact topology; open books; contact topology},
language = {eng},
number = {1},
pages = {139-157},
publisher = {Association des Annales de l’institut Fourier},
title = {Open books on contact five-manifolds},
url = {http://eudml.org/doc/10307},
volume = {58},
year = {2008},
}

TY - JOUR
AU - van Koert, Otto
TI - Open books on contact five-manifolds
JO - Annales de l’institut Fourier
PY - 2008
PB - Association des Annales de l’institut Fourier
VL - 58
IS - 1
SP - 139
EP - 157
AB - By using open book techniques we give an alternative proof of a theorem about the existence of contact structures on five-manifolds due to Geiges. The theorem asserts that simply-connected five-manifolds admit a contact structure in every homotopy class of almost contact structures.
LA - eng
KW - Contact topology; open books; contact topology
UR - http://eudml.org/doc/10307
ER -

References

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  1. N. A’Campo, Feuilletages de codimension 1 sur des variétés de dimension 5 , C. R. Acad. Sci. Paris Sér. A-B 273 (1971), A603-A604 Zbl0221.57009
  2. D. Barden, Simply connected five-manifolds, Ann. of Math. (2) 82 (1965), 365-385 Zbl0136.20602MR184241
  3. H. Geiges, Contact structures on 1 -connected 5 -manifolds, Mathematika 38 (1991), 303-311 Zbl0724.57017MR1147828
  4. E. Giroux, J. Mohsen, Contact structures and symplectic fibrations over the circle 
  5. R. Gompf, Handlebody construction of Stein surfaces, Ann. of Math. (2) 148 (1998), 619-693 Zbl0919.57012MR1668563
  6. R. Gompf, A. Stipsicz, 4 -manifolds and Kirby calculus, 20 (1999), American Mathematical Society, Providence, RI Zbl0933.57020MR1707327
  7. F. Hirzebruch, K. Mayer, O ( n ) -Mannigfaltigkeiten, exotische Sphären und Singularitäten, (1968), Springer-Verlag, Berlin Zbl0172.25304MR229251
  8. F. Pham, Formules de Picard-Lefschetz généralisées et ramification des intégrales, Bull. Soc. Math. France 93 (1965), 333-367 Zbl0192.29701MR195868
  9. R. Randell, The homology of generalized Brieskorn manifolds, Topology 14 (1975), 347-355 Zbl0317.57012MR413149
  10. W. Thurston, H. Winkelnkemper, On the existence of contact forms, Proc. Amer. Math. Soc. 52 (1975), 345-347 Zbl0312.53028MR375366
  11. H-C. Wang, Homology of fibre bundles Duke, Math Journal 16 (1949), 33-38 Zbl0033.30801MR28580

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