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Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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A proof of the compact leaf conjecture for foliated bundles
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by R. Uomini PDF
Proc. Amer. Math. Soc. 59 (1976), 381-382 Request permission

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
  • K. deCesare and T. Nagano, On compact foliations, Differential geometry (Proc. Sympos. Pure Math., Vol. XXVII, Part 1, 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
  • D. Montgomery and C. T. Yang (personal communication).
  • Deane Montgomery and Leo Zippin, Topological transformation groups, Interscience Publishers, New York-London, 1955. MR 0073104
  • D. Sullivan, A counterexample to the compact leaf conjecture (to appear).
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Additional Information
  • © Copyright 1976 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 59 (1976), 381-382
  • MSC: Primary 57D30
  • DOI: https://doi.org/10.1090/S0002-9939-1976-0418120-0
  • MathSciNet review: 0418120