Contact topology and the structure of 5-manifolds with π 1 = 2
Annales de l'Institut Fourier, Volume 48 (1998) no. 4, p. 1167-1188

We prove a structure theorem for closed, orientable 5-manifolds M with fundamental group π 1 (M)= 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 2 -quotients of S 2 ×S 3 .

Nous démontrons un théorème relatif à la structure des variétés M fermées, orientables, de dimension 5 avec groupe fondamental π 1 (M)= 2 et deuxième classe de Stiefel-Whitney égale à zéro sur H 2 (M). Ce théorème est alors utilisé pour construire des structures de contact sur ces variétés en appliquant la chirurgie de contact à de faux espaces projectifs et certains quotients de S 2 ×S 3 par une involution.

@article{AIF_1998__48_4_1167_0,
     author = {Geiges, Hansj\"org and Thomas, Charles B.},
     title = {Contact topology and the structure of 5-manifolds with $\pi \_1={\mathbb {Z}}\_2$},
     journal = {Annales de l'Institut Fourier},
     publisher = {Association des Annales de l'institut Fourier},
     volume = {48},
     number = {4},
     year = {1998},
     pages = {1167-1188},
     doi = {10.5802/aif.1653},
     zbl = {0912.57020},
     mrnumber = {2000a:57069},
     language = {en},
     url = {http://www.numdam.org/item/AIF_1998__48_4_1167_0}
}
Geiges, Hansjörg; Thomas, Charles B. Contact topology and the structure of 5-manifolds with $\pi _1={\mathbb {Z}}_2$. Annales de l'Institut Fourier, Volume 48 (1998) no. 4, pp. 1167-1188. doi : 10.5802/aif.1653. http://www.numdam.org/item/AIF_1998__48_4_1167_0/

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