The closed leaf index of foliated manifolds
Authors:
Lawrence Conlon and Sue Goodman
Journal:
Trans. Amer. Math. Soc. 233 (1977), 205-221
MSC:
Primary 57D30
DOI:
https://doi.org/10.1090/S0002-9947-1977-0467768-1
MathSciNet review:
0467768
Full-text PDF Free Access
Abstract | References | Similar Articles | Additional Information
Abstract: For M a closed, connected, oriented 3-manifold, a topological invariant is computed from the cohomology ring ${H^\ast }(M;{\mathbf {Z}})$ that provides an upper bound to the number of topologically distinct types of closed leaves any smooth transversely oriented foliation of M can contain. In general, this upper bound is best possible.
- Lawrence Conlon and Sue Goodman, Opening closed leaves in foliated $3$-manifolds, Topology 14 (1975), 59–61. MR 358803, DOI https://doi.org/10.1016/0040-9383%2875%2990035-X
- Sue Goodman, Closed leaves in foliated $3$-manifolds, Proc. Nat. Acad. Sci. U.S.A. 71 (1974), 4414–4415. MR 350751, DOI https://doi.org/10.1073/pnas.71.11.4414
- S. P. Novikov, The topology of foliations, Trudy Moskov. Mat. Obšč. 14 (1965), 248–278 (Russian). MR 0200938
- Charles C. Pugh, A generalized Poincaré index formula, Topology 7 (1968), 217–226. MR 229254, DOI https://doi.org/10.1016/0040-9383%2868%2990002-5 P. A. Schweitzer, Codimension one plane fields and foliations, Differential Geometry (Proc. Sympos. Pure Math., vol. 27, part 1), Amer. Math. Soc., Providence, R. I., 1975, pp. 311-312.
- W. P. Thurston, Existence of codimension-one foliations, Ann. of Math. (2) 104 (1976), no. 2, 249–268. MR 425985, DOI https://doi.org/10.2307/1971047
- John W. Wood, Foliations on $3$-manifolds, Ann. of Math. (2) 89 (1969), 336–358. MR 248873, DOI https://doi.org/10.2307/1970673
Retrieve articles in Transactions of the American Mathematical Society with MSC: 57D30
Retrieve articles in all journals with MSC: 57D30
Additional Information
Article copyright:
© Copyright 1977
American Mathematical Society