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Foliations and spinnable structures on manifolds

Itiro Tamura — 1973

Annales de l'institut Fourier

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 ( 2 n + 1 ) -dimensional differentiable manifold ( n 3 ) , then M admits a spinnable structure with axis S 2 n + 1 . Making use of the codimension-one foliation on S 2 n + 1 , this yields that M admits a codimension-foliation....

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