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

top
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

top

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

top
  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

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

                
Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.