Stability of foliations of 3-manifolds by circles

Kazuhiko FUKUI

doi:10.2969/jmsj/03910117

Kazuhiko FUKUI

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JOURNAL FREE ACCESS

1987 Volume 39 Issue 1 Pages 117-126

DOI https://doi.org/10.2969/jmsj/03910117

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Published: 1987 Received: March 29, 1985 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: SUBTITLE Details: Wrong : Dedicated to Professor Itiro Tamura on his 60th birthday

Date of correction: October 20, 2006 Reason for correction: - Correction: CITATION Details: Wrong : 1) D. Epstein, Periodic flows on three manifolds, Ann. of Math., 95 (1976), 68-82.
2) D. Epstein, A topology for the space of foliations, Geometry and Topology, Lecture Notes in Math., 597, Springer, 1976, pp. 132-150.
3) K. Fukui, Perturbations of compact foliations, Proc. Japan Acad. Ser. A, 58 (1982), 341-344.
4) F. Fuller, An index of fixed point type for periodic orbits, Amer. J. Math., 89 (1967), 133-148.
5) M. Hirsch, Stability of compact leaves of foliations, Dynamical Systems, Academic Press, 1971, pp. 135-155.
6) R. Langevin and H. Rosenberg, On stability of compact leaves and fibrations, Topology, 16 (1977), 107-112.
7) R. Langevin and H. Rosenberg, Integral perturbations of fibrations and a theorem of Seifert, Differential Topology, Foliations and Gelfand-Fuks Cohomology, Lecture Notes in Math., 652, Springer, 1978, pp. 122-127.
8) J. Plante, Stability of codimension one foliations by compact leaves, Topology, 22 (1983), 173-177.
9) G. Reeb, Sur certaines propriétés topologiques des variétés feuilletées, Actualités Sci. Indust., 1183, Hermann, Paris, 1952.
10) I. Satake, The Gauss-Bonnet theorem for V-manifolds, J. Math. Soc. Japan, 9 (1957), 464-492.
11) H. Seifert, Closed integral curves in 3-spaces and isotopic two dimensional deformations, Proc. Amer. Math. Soc., 1 (1950), 287-302.
12) D. Stowe, The stationary set of a group action, Proc. Amer. Math. Soc., 79 (1980), 139-146,
13) W, Thurston, A generalization of the Reeb stability theorem, Topology, 13 (1974), 347-352.

Right : [1] D. Epstein, Periodic flows on three manifolds, Ann. of Math., 95 (1976), 68-82.
[2] D. Epstein, A topology for the space of foliations, Geometry and Topology, Lecture Notes in Math., 597, Springer, 1976, pp. 132-150.
[3] K. Fukui, Perturbations of compact foliations, Proc. Japan Acad. Ser. A, 58 (1982), 341-344.
[4] F. Fuller, An index of fixed point type for periodic orbits, Amer. J. Math., 89 (1967), 133-148.
[5] M. Hirsch, Stability of compact leaves of foliations, Dynamical Systems, Academic Press, 1971, pp. 135-155.
[6] R. Langevin and H. Rosenberg, On stability of compact leaves and fibrations, Topology, 16 (1977), 107-112.
[7] R. Langevin and H. Rosenberg, Integral perturbations of fibrations and a theorem of Seifert, Differential Topology, Foliations and Gelfand-Fuks Cohomology, Lecture Notes in Math., 652, Springer, 1978, pp. 122-127.
[8] J. Plante, Stability of codimension one foliations by compact leaves, Topology, 22 (1983), 173-177.
[9] G. Reeb, Sur certaines propriétés topologiques des variétés feuilletées, Actualités Sci. Indust., 1183, Hermann, Paris, 1952.
[10] I. Satake, The Gauss-Bonnet theorem for V-manifolds, J. Math. Soc. Japan, 9 (1957), 464-492.
[11] H. Seifert, Closed integral curves in 3-spaces and isotopic two dimensional deformations, Proc. Amer. Math. Soc., 1 (1950), 287-302.
[12] D. Stowe, The stationary set of a group action, Proc. Amer. Math. Soc., 79 (1980), 139-146,
[13] W. Thurston, A generalization of the Reeb stability theorem, Topology, 13 (1974), 347-352.

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