Holonomy invariant cochains for foliations
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- by John M. Franks
- Proc. Amer. Math. Soc. 62 (1977), 161-164
- DOI: https://doi.org/10.1090/S0002-9939-1977-0431198-4
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Abstract:
The notion of a holonomy invariant cochain for a foliation is developed generalizing the idea of a holonomy invariant measure. An example is given on a foliation in which every leaf has exponential growth, and it is shown that if the inclusion of every leaf is trivial on ${H_1}$ for a codimension one transversally oriented foliation, then holonomy invariant cochains generate all of the one dimensional cohomology.References
- M. Hirsch, A stable analytic foliation with only exceptional minimal sets, Dynamical Systems-Warwick 1974, Lecture Notes in Math., vol. 468, Springer-Verlag, Berlin and New York, 1975, pp. 9-10.
- Morris W. Hirsch and William P. Thurston, Foliated bundles, invariant measures and flat manifolds, Ann. of Math. (2) 101 (1975), 369–390. MR 370615, DOI 10.2307/1970996
- J. F. Plante, Foliations with measure preserving holonomy, Ann. of Math. (2) 102 (1975), no. 2, 327–361. MR 391125, DOI 10.2307/1971034
- David Ruelle and Dennis Sullivan, Currents, flows and diffeomorphisms, Topology 14 (1975), no. 4, 319–327. MR 415679, DOI 10.1016/0040-9383(75)90016-6
- William Thurston, The theory of foliations of codimension greater than one, Comment. Math. Helv. 49 (1974), 214–231. MR 370619, DOI 10.1007/BF02566730
Bibliographic Information
- © Copyright 1977 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 62 (1977), 161-164
- MSC: Primary 57D30
- DOI: https://doi.org/10.1090/S0002-9939-1977-0431198-4
- MathSciNet review: 0431198