Stability and instability of certain foliations of {4}-manifolds by closed orientable surfaces
Kazuhiko Fukui
Source: Publ. Res. Inst. Math. Sci. Volume 22, Number 6 (1986), 1155-1171.
Primary Subjects: 57R30
Secondary Subjects: 57N13
Full-text: Open access
Links and Identifiers
Permanent link to this document: http://projecteuclid.org/euclid.prims/1195177067
Mathematical Reviews number (MathSciNet):
MR880002
Zentralblatt MATH identifier:
0623.57017
Digital Object Identifier: doi:10.2977/prims/1195177067
References
[1] Edwards, R., Millett K. and Sullivan, D., Foliations with all leaves compact, Topology, 16 (1977), 13-32.
Mathematical Reviews (MathSciNet):
MR438353
Zentralblatt MATH:
0356.57022
[2] Epstein, D., Periodic flows on three-manifolds, Ann. of Math., 95 (1976), 68-82.
Mathematical Reviews (MathSciNet):
MR288785
Zentralblatt MATH:
0231.58009
[3] Epstein, D., Foliations with all leaves compact, Ann, Insl. Fourier, Grenoble, 26 (1976), 265-282.
Mathematical Reviews (MathSciNet):
MR420652
Zentralblatt MATH:
0313.57017
[4] Fukui, K., Perturbations of compact foliations, Proc. Japan Acad., 58 Ser. A (1982), 341-344.
Mathematical Reviews (MathSciNet):
MR683259
Zentralblatt MATH:
0531.57024
[5] Fukui, K., Stability of foliations of 3-manifolds by circles, to appear in J. M. S. Japan.
Mathematical Reviews (MathSciNet):
MR867990
Zentralblatt MATH:
0608.57021
[6] Fuller, F., An index of fixed point type for periodic orbits, Atner. J. of Math., 89 (1967), 133-143.
Mathematical Reviews (MathSciNet):
MR209600
Zentralblatt MATH:
0152.40204
[7] Hirsch, M., Stability of compact leaves of foliations, Dynamical Systems, Acad. Press, (1971), 135-155.
Mathematical Reviews (MathSciNet):
MR334236
Zentralblatt MATH:
0272.57015
[8] Langevin R. and Rosenberg, E. L., On stability of compact leaves and fibrations, Topology, 16 (1977), 107-112.
Mathematical Reviews (MathSciNet):
MR461523
Zentralblatt MATH:
0346.57009
[9] Langevin R. and Rosenberg, E. L., Integral perturbations of fibrations and a theorem of Seifert, Differential topology, foliations and Gelfand-Fuks cohomology, Lecture notes in Math., 652 (1978), 122-127.
Mathematical Reviews (MathSciNet):
MR505655
Zentralblatt MATH:
0382.57011
[10] Plante, J., Stability of codimension one foliations by compact leaves, Topology, 22 (1983), 173-177.
Mathematical Reviews (MathSciNet):
MR683758
Zentralblatt MATH:
0523.57018
[11] Reeb, G., Sur certaines proprietes topologiques des varietes feuilletees, Act. Sc. et Ind., 1183, Herman, Paris, 1952.
Mathematical Reviews (MathSciNet):
MR55692
Zentralblatt MATH:
0049.12602
[12] Satake, I., The Gauss-Bonnet theorem for F-manifolds, J. M. S. Japan, 9-4 (1957), 464-492.
Mathematical Reviews (MathSciNet):
MR95520
Zentralblatt MATH:
0080.37403
[13] Seifert, H., Closed integral curves in 3-spaces and isotopic two dimensional deformations, Proc. A. M.S., I (1950), 287-302.
Mathematical Reviews (MathSciNet):
MR37508
Zentralblatt MATH:
0039.40002
[14] Siegel, C. L., Note on differential equations on the torus, Ann. of Math., 46 (1945), 423-428.
Mathematical Reviews (MathSciNet):
MR13177
Zentralblatt MATH:
0061.19510
[15] Stowe, D., The stationary set of a group action, Proc. A. M. S., 79 (1980), 139-146.
Mathematical Reviews (MathSciNet):
MR560600
Zentralblatt MATH:
0454.57027
[16] Thurston, W., A generalization of the Reeb stability theorem, Topology, 15 (1974), 347-352.
Mathematical Reviews (MathSciNet):
MR356087
Zentralblatt MATH:
0305.57025
[17] Vogt, E., Stable foliations of 4-manifolds by closed surfaces, Inv. Math., 22 (1973), 321-348.
Mathematical Reviews (MathSciNet):
MR356064
Zentralblatt MATH:
0268.57012
Publications of the Research Institute for Mathematical Sciences