Contact topology and the structure of 5-manifolds with π 1 = ℤ 2

Hansjörg Geiges; Charles B. Thomas

Annales de l'institut Fourier (1998)

  • Volume: 48, Issue: 4, page 1167-1188
  • ISSN: 0373-0956

Abstract

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We prove a structure theorem for closed, orientable 5-manifolds M with fundamental group π 1 ( M ) = ℤ 2 and second Stiefel-Whitney class equal to zero on H 2 ( M ) . This structure theorem is then used to construct contact structures on such manifolds by applying contact surgery to fake projective spaces and certain ℤ 2 -quotients of  S 2 × S 3 .

How to cite

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Geiges, Hansjörg, and Thomas, Charles B.. "Contact topology and the structure of 5-manifolds with $\pi _1={\mathbb {Z}}_2$." Annales de l'institut Fourier 48.4 (1998): 1167-1188. <http://eudml.org/doc/75313>.

@article{Geiges1998,
abstract = {We prove a structure theorem for closed, orientable 5-manifolds $M$ with fundamental group $\pi _1(M)=\{\Bbb Z\}_2$ and second Stiefel-Whitney class equal to zero on $H_2(M)$. This structure theorem is then used to construct contact structures on such manifolds by applying contact surgery to fake projective spaces and certain $\{\Bbb Z\}_2$-quotients of $S^2\times S^3$.},
author = {Geiges, Hansjörg, Thomas, Charles B.},
journal = {Annales de l'institut Fourier},
keywords = {surgery; contact structures; contact surgery; involutions; Brieskorn manifolds; characteristic submanifold; pin cobordism},
language = {eng},
number = {4},
pages = {1167-1188},
publisher = {Association des Annales de l'Institut Fourier},
title = {Contact topology and the structure of 5-manifolds with $\pi _1=\{\mathbb \{Z\}\}_2$},
url = {http://eudml.org/doc/75313},
volume = {48},
year = {1998},
}

TY - JOUR
AU - Geiges, Hansjörg
AU - Thomas, Charles B.
TI - Contact topology and the structure of 5-manifolds with $\pi _1={\mathbb {Z}}_2$
JO - Annales de l'institut Fourier
PY - 1998
PB - Association des Annales de l'Institut Fourier
VL - 48
IS - 4
SP - 1167
EP - 1188
AB - We prove a structure theorem for closed, orientable 5-manifolds $M$ with fundamental group $\pi _1(M)={\Bbb Z}_2$ and second Stiefel-Whitney class equal to zero on $H_2(M)$. This structure theorem is then used to construct contact structures on such manifolds by applying contact surgery to fake projective spaces and certain ${\Bbb Z}_2$-quotients of $S^2\times S^3$.
LA - eng
KW - surgery; contact structures; contact surgery; involutions; Brieskorn manifolds; characteristic submanifold; pin cobordism
UR - http://eudml.org/doc/75313
ER -

References

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