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Classification des variétés différentiables, $(n - 1)$ -connexes, sans torsion, de dimension $2 n + 1$

Itiro Tamura

Séminaire Henri Cartan

Every Odd Dimensional Homotopy Sphere has a Foliation of Codimension One

Itiro Tamura — 1972

Commentarii mathematici Helvetici

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 $(n \geq 3)$ , 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....