Foliations and spinnable structures on manifolds

• Volume: 23, Issue: 2, page 197-214
• ISSN: 0373-0956

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Abstract

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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 $\left(n-1\right)$-connected $\left(2n+1\right)$-dimensional differentiable manifold $\left(n\ge 3\right)$, 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.

How to cite

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Tamura, Itiro. "Foliations and spinnable structures on manifolds." Annales de l'institut Fourier 23.2 (1973): 197-214. <http://eudml.org/doc/74123>.

@article{Tamura1973,
abstract = {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 $(n\ge 3)$, 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.},
author = {Tamura, Itiro},
journal = {Annales de l'institut Fourier},
language = {eng},
number = {2},
pages = {197-214},
publisher = {Association des Annales de l'Institut Fourier},
title = {Foliations and spinnable structures on manifolds},
url = {http://eudml.org/doc/74123},
volume = {23},
year = {1973},
}

TY - JOUR
AU - Tamura, Itiro
TI - Foliations and spinnable structures on manifolds
JO - Annales de l'institut Fourier
PY - 1973
PB - Association des Annales de l'Institut Fourier
VL - 23
IS - 2
SP - 197
EP - 214
AB - 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 $(n\ge 3)$, 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.
LA - eng
UR - http://eudml.org/doc/74123
ER -

References

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9. [9] T. MIZUTANI, Remarks on codimension one foliations of spheres, J. Math. Soc. Japan, 24 (1972), 732-735. Zbl0238.57014MR46 #2689
10. [10] G. REEB, Sur certaines propriétés topologiques des variétés feuilletées, Actualités Sci. Indust., No. 1183, Hermann, Paris, 1952. Zbl0049.12602MR14,1113a
11. [11] S. SMALE, On the structure of manifolds, Amer. J. Math., 84 (1962), 387-399. Zbl0109.41103MR27 #2991
12. [12] I. TAMURA, Every odd dimensional homotopy sphere has a foliation of codimension one, Comm. Math. Helv., 47 (1972), (voir Comm. Math.). Zbl0249.57013MR47 #5887
13. [13] I. TAMURA, Spinnable structures on differentiable manifolds, Proc. Japan Acad., 48 (1972), 293-296. Zbl0252.57009MR47 #7756
14. [14] H. E. WINKELNKEMPER, Manifolds as open books (to appear). Zbl0269.57011

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