Foliations with nonorientable leaves
Authors:
W. G. Dwyer, D. B. Ellis and R. H. Szczarba
Journal:
Proc. Amer. Math. Soc. 89 (1983), 733-737
MSC:
Primary 57R30; Secondary 57R99
DOI:
https://doi.org/10.1090/S0002-9939-1983-0719007-X
MathSciNet review:
719007
Full-text PDF Free Access
Abstract | References | Similar Articles | Additional Information
Abstract: We prove that a codimension one foliation of an orientable paracompact manifold has at most a countable number of nonorientable leaves. We also give an example of a codimension one foliation of a compact orientable manifold with an infinite number of nonorientable leaves.
- [1] D. B. A. Epstein, K. C. Millett, and D. Tischler, Leaves without holonomy, J. London Math. Soc. (2) 16 (1977), no. 3, 548–552. MR 0464259, https://doi.org/10.1112/jlms/s2-16.3.548
- [2] Daniel A. Marcus, Number fields, Springer-Verlag, New York-Heidelberg, 1977. Universitext. MR 0457396
- [3] William S. Massey, Algebraic topology: An introduction, Harcourt, Brace & World, Inc., New York, 1967. MR 0211390
- [4] J. F. Plante, Foliations with measure preserving holonomy, Ann. of Math. (2) 102 (1975), no. 2, 327–361. MR 0391125, https://doi.org/10.2307/1971034
Retrieve articles in Proceedings of the American Mathematical Society with MSC: 57R30, 57R99
Retrieve articles in all journals with MSC: 57R30, 57R99
Additional Information
DOI:
https://doi.org/10.1090/S0002-9939-1983-0719007-X
Article copyright:
© Copyright 1983
American Mathematical Society