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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: 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.

References [Enhancements On Off] (What's this?)

  • 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
  • R. Edwards, K. Millet and D. Sullivan, On foliations with compact leaves (to appear).
  • 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
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  • D. Sullivan, A counterexample to the compact leaf conjecture (to appear).

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Keywords: Foliations, fiber bundles, periodic diffeomorphism, finite group actions
Article copyright: © Copyright 1976 American Mathematical Society