no. 2
Foliations and spinnable structures on manifolds
Annales de l'Institut Fourier, Tome 23 (1973) no. 2, pp. 197-214.

On étudie une structure nouvelle, dite spinnable, sur des variétés différentielles. On dit qu’une variété différentielle est spinnable si elle peut tourner autour d’une sous-variété de codimension 2 qui s’appelle l’axe, comme une toupie.

Le résultat principal de cet article est le suivant : soit M une variété différentielle compacte, (n-1)-connexe de dimension 2n+1(n≥3), du feuilletage de codimension 1 sur S 2n+1 , on en déduit que M admet une feuilletage de codimension 1.

In this paper we study a new structure, called a spinnable structure, on a differentiable manifold. Roughly speaking, a differentiable manifold is spinnable if it can spin around a codimension 2 submanifold, called the axis, as if the top spins.

The main result is the following: let M be a compact (n-1)-connected (2n+1)-dimensional differentiable manifold (n≥3), then M admits a spinnable structure with axis S 2n+1 . Making use of the codimension-one foliation on S 2n+1 , this yields that M admits a codimension-foliation.

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     author = {Tamura, Itiro},
     title = {Foliations and spinnable structures on manifolds},
     journal = {Annales de l'Institut Fourier},
     pages = {197--214},
     publisher = {Institut Fourier},
     address = {Grenoble},
     volume = {23},
     number = {2},
     year = {1973},
     doi = {10.5802/aif.468},
     zbl = {0269.57012},
     mrnumber = {50 #14788},
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Tamura, Itiro. Foliations and spinnable structures on manifolds. Annales de l'Institut Fourier, Tome 23 (1973) no. 2, pp. 197-214. doi : 10.5802/aif.468. https://aif.centre-mersenne.org/articles/10.5802/aif.468/

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