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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

A proof of the compact leaf conjecture for foliated bundles


Author: R. Uomini
Journal: Proc. Amer. Math. Soc. 59 (1976), 381-382
MSC: Primary 57D30
MathSciNet review: 0418120
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Abstract | References | Similar Articles | Additional Information

Abstract: Given an oriented fiber bundle $ M$ whose fiber is a connected, $ m$-dimensional manifold, and a codimension $ n$ foliation of $ M$ which is transverse to the fibers of $ M$ and all of whose leaves are compact, we will show that there is an upper bound on the orders of the holonomy groups of the leaves.


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  • [1] K. deCesare and T. Nagano, On compact foliations, Differential geometry (Proc. Sympos. Pure Math., Vol. XXVII, Stanford Univ., Stanford, Calif., 1973) Amer. Math. Soc., Providence, R. I., 1975, pp. 277–281. MR 0377924 (51 #14093)
  • [2] R. Edwards, K. Millet and D. Sullivan, On foliations with compact leaves (to appear).
  • [3] A. G. Kurosh, The theory of groups, Chelsea Publishing Co., New York, 1960. Translated from the Russian and edited by K. A. Hirsch. 2nd English ed. 2 volumes. MR 0109842 (22 #727)
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  • [5] Deane Montgomery and Leo Zippin, Topological transformation groups, Interscience Publishers, New York-London, 1955. MR 0073104 (17,383b)
  • [6] D. Sullivan, A counterexample to the compact leaf conjecture (to appear).

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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1976-0418120-0
PII: S 0002-9939(1976)0418120-0
Keywords: Foliations, fiber bundles, periodic diffeomorphism, finite group actions
Article copyright: © Copyright 1976 American Mathematical Society