Morse theory for codimension-one foliations
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- by Steven C. Ferry and Arthur G. Wasserman PDF
- Trans. Amer. Math. Soc. 298 (1986), 227-240 Request permission
Abstract:
It is shown that a smooth codimension-one foliation on a compact simply-connected manifold has a compact leaf if and only if every smooth real-valued function on the manifold has a cusp singularity.References
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S. Ferry, Codimension one Morse theory, Thesis, Univ. of Michigan, 1973.
- André Haefliger, Quelques remarques sur les applications différentiables d’une surface dans le plan, Ann. Inst. Fourier (Grenoble) 10 (1960), 47–60 (French). MR 116357
- Allen Hatcher and John Wagoner, Pseudo-isotopies of compact manifolds, Astérisque, No. 6, Société Mathématique de France, Paris, 1973. With English and French prefaces. MR 0353337
- Harold I. Levine, Elimination of cusps, Topology 3 (1965), no. suppl, suppl. 2, 263–296. MR 176484, DOI 10.1016/0040-9383(65)90078-9 —, Singularities of differentiable mappings, Mimeographed notes, Math. Inst., Bonn Univ., 1959.
- J. Milnor, Morse theory, Annals of Mathematics Studies, No. 51, Princeton University Press, Princeton, N.J., 1963. Based on lecture notes by M. Spivak and R. Wells. MR 0163331
- S. P. Novikov, The topology of foliations, Trudy Moskov. Mat. Obšč. 14 (1965), 248–278 (Russian). MR 0200938
- R. Thom, Les singularités des applications différentiables, Ann. Inst. Fourier (Grenoble) 6 (1955/56), 43–87 (French). MR 87149
- René Thom, Généralisation de la théorie de Morse aux variétés feuilletées, Ann. Inst. Fourier (Grenoble) 14 (1964), no. fasc. 1, 173–189 (French). MR 170352
- Y. H. Wan, Morse theory for two functions, Topology 14 (1975), no. 3, 217–228. MR 377981, DOI 10.1016/0040-9383(75)90002-6
- Hassler Whitney, On singularities of mappings of euclidean spaces. I. Mappings of the plane into the plane, Ann. of Math. (2) 62 (1955), 374–410. MR 73980, DOI 10.2307/1970070
Additional Information
- © Copyright 1986 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 298 (1986), 227-240
- MSC: Primary 57R30; Secondary 57R45, 58C27
- DOI: https://doi.org/10.1090/S0002-9947-1986-0857441-5
- MathSciNet review: 857441