Foliations and foliated cobordisms of spheres in codimension one

Tadayoshi MIZUTANI

doi:10.2969/jmsj/02720264

Tadayoshi MIZUTANI

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JOURNAL FREE ACCESS

1975 Volume 27 Issue 2 Pages 264-280

DOI https://doi.org/10.2969/jmsj/02720264

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Published: 1975 Received: February 26, 1974 Available on J-STAGE: October 20, 2006 Accepted: - Advance online publication: - Revised: -
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Date of correction: October 20, 2006 Reason for correction: - Correction: CITATION Details: Wrong : 1) N. A'Campo, Feuilletages de codimension 1 sur les variétés de dimension 5, C. R. Acad. Sci. Paris, 273 (1971), 603-604.
2) J. W. Alexander, A lemma on systems of knotted curves, Proc. Nat. Acad. Sci., 9 (1923), 93-95.
3) E. Brieskorn, Beispiele zur Differentialtopologie von Singularitäten, Invent. Math., 2 (1966), 1-14.
4) A.H. Durfee, Foliations of odd-dimensional spheres, Ann. of Math., 92 (1972), 407-411.
5) K. Fukui, Codimension 1 foliations on simply connected 5-manifolds, to appear.
6) A. Haefliger, Variétés feuilletées, Ann. Scuola Norm. Sup. Pisa, 16 (1962), 367-397.
7) H. Imanishi, Sur l'existence des feuilletages S¹-invariants, J. Math. Kyoto Univ., 12 (1972), 297-307.
8) M. Kato, A classification of simple spinnable structures on a 1-connected Alexander manifold, J. Math. Soc. Japan, 26 (1974), 454-463.
9) H. B. Lawson, Codimension-one foliations of spheres, Ann. of Math., 94 (1971), 494-503.
10) J. Milnor, On the existence of a connection with zero curvature, Comment. Math. Helv., 32 (1958), 215-223.
11) T. Mizutani, Remarks on codimension one foliations of spheres, J. Math. Soc. Japan, 24 (1972), 732-735.
12) T. Mizutani, Foliated cobordisms of S³ and examples of foliated 4-manifolds, Topology, 13 (1974), 353-362.
13) T. Mizutani and I. Tamura, Foliations of even dimensional manifolds, Proccedings of the International Conference on Manifolds and Related Topics in Topology, Tokyo, 1973.
14) K. Sakamoto, Milnor fiberings and their characteristic maps, Procceedings of the International Conference on Manifolds and Related Topics it Topology, Tokyo, 1973.
15) S. Smale, On the structure of manifolds, Amer. J. Math., 84 (1962), 387-399.
16) I. Tamura, Every odd dimensional homotopy sphere has a foliation of codimension one, Comm. Math. Helv., 47 (1972), 164-170.
17) I. Tamura, Spinnable structures on differentiable maifolds, Proc. Japan Acad., 48 (1972), 293-296.
18) I. Tamura, Foliations of total spaces of sphere bundles over spheres, J. Math. Soc. Japan, 24 (1972), 689-700.
19) I. Tamura, Foliations and spinnable structures on manifolds, Actes du Colloque international d'Analyse et Topologie Différentielles de Strasbourg, Ann. Inst. Fourier, 23 (1973), 197-214.
20) I. Tamura, Specially spinnable manifolds, Proceedings of the International Conference on Manifolds and Related Topics in Topology, Tokyo, 1973.
21) I. Tamura and T. Mizutani,
22) W. Thurston, Noncobordant Foliations of S³, Bull. Amer. Math. Soc., 78 (1972), 511-514.
23) H. E. Winkelnkemper, Equators of manifolds and the action of Θⁿ, Ph. D. Thesis, Princeton Univ., Princeton, New Jersey, 1970.
24) H. E. Winkelnkemper, Manifolds as open books, Bull. Amer. Math. Soc., 79 (1973), 45-51.
25) J. Wood, Bundles with totally disconnected structure group, Comm. Math. Helv., 46 (1971), 257-273.

Right : [1] N. A'Campo, Feuilletages de codimension 1 sur les variétés de dimension 5, C. R. Acad. Sci. Paris, 273 (1971), 603-604.
[2] J. W. Alexander, A lemma on systems of knotted curves, Proc. Nat. Acad. Sci., 9 (1923), 93-95.
[3] E. Brieskorn, Beispiele zur Differentialtopologie von Singularitäten, Invent. Math., 2 (1966), 1-14.
[4] A.H. Durfee, Foliations of odd-dimensional spheres, Ann. of Math., 92 (1972), 407-411.
[5] K. Fukui, Codimension 1 foliations on simply connected 5-manifolds, to appear.
[6] A. Haefliger, Variétés feuilletées, Ann. Scuola Norm. Sup. Pisa, 16 (1962), 367-397.
[7] H. Imanishi, Sur l'existence des feuilletages S¹-invariants, J. Math. Kyoto Univ., 12 (1972), 297-307.
[8] M. Kato, A classification of simple spinnable structures on a 1-connected Alexander manifold, J. Math. Soc. Japan, 26 (1974), 454-463.
[9] H. B. Lawson, Codimension-one foliations of spheres, Ann. of Math., 94 (1971), 494-503.
[10] J. Milnor, On the existence of a connection with zero curvature, Comment. Math. Helv., 32 (1958), 215-223.
[11] T. Mizutani, Remarks on codimension one foliations of spheres, J. Math. Soc. Japan, 24 (1972), 732-735.
[12] T. Mizutani, Foliated cobordisms of S³ and examples of foliated 4-manifolds, Topology, 13 (1974), 353-362.
[13] T. Mizutani and I. Tamura, Foliations of even dimensional manifolds, Proccedings of the International Conference on Manifolds and Related Topics in Topology, Tokyo, 1973.
[14] K. Sakamoto, Milnor fiberings and their characteristic maps, Procceedings of the International Conference on Manifolds and Related Topics it Topology, Tokyo, 1973.
[15] S. Smale, On the structure of manifolds, Amer. J. Math., 84 (1962), 387-399.
[16] I. Tamura, Every odd dimensional homotopy sphere has a foliation of codimension one, Comm. Math. Helv., 47 (1972), 164-170.
[17] I. Tamura, Spinnable structures on differentiable maifolds, Proc. Japan Acad., 48 (1972), 293-296.
[18] I. Tamura, Foliations of total spaces of sphere bundles over spheres, J. Math. Soc. Japan, 24 (1972), 689-700.
[19] I. Tamura, Foliations and spinnable structures on manifolds, Actes du Colloque international d'Analyse et Topologie Différentielles de Strasbourg, Ann. Inst. Fourier, 23 (1973), 197-214.
[20] I. Tamura, Specially spinnable manifolds, Proceedings of the International Conference on Manifolds and Related Topics in Topology, Tokyo, 1973.
[21] I. Tamura and T. Mizutani,
[22] W. Thurston, Noncobordant Foliations of S³, Bull. Amer. Math. Soc., 78 (1972), 511-514.
[23] H. E. Winkelnkemper, Equators of manifolds and the action of Θⁿ, Ph. D. Thesis, Princeton Univ., Princeton, New Jersey, 1970.
[24] H. E. Winkelnkemper, Manifolds as open books, Bull. Amer. Math. Soc., 79 (1973), 45-51.
[25] J. Wood, Bundles with totally disconnected structure group, Comm. Math. Helv., 46 (1971), 257-273.

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