A proof of the compact leaf conjecture for foliated bundles
Proc. Amer. Math. Soc. 59 (1976), 381-382
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Abstract: Given an oriented fiber bundle whose fiber is a connected, -dimensional manifold, and a codimension foliation of which is transverse to the fibers of 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.
deCesare and T.
Nagano, On compact foliations, Differential geometry (Proc.
Sympos. Pure Math., Vol. XXVII, Stanford Univ., Stanford, Calif., 1973),
Part 1, Amer. Math. Soc., Providence, R. I., 1975, pp. 277–281.
0377924 (51 #14093)
R. Edwards, K. Millet and D. Sullivan, On foliations with compact leaves (to appear).
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).
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).
- K. de Cesare and T. Nagano, On compact foliations, Differential Geometry (Proc. Sympos. Pure Math., vol. 27, Part 1), Amer. Math. Soc., Providence, R.I., 1975, pp. 277-281. MR 0377924 (51:14093)
- R. Edwards, K. Millet and D. Sullivan, On foliations with compact leaves (to appear).
- A. Kuroš, The theory of groups, Vol. 2, OGIZ, Moscow, 1944; English transl. of 2nd ed., Chelsea, New York, 1960. MR 22 #727. MR 0109842 (22:727)
- D. Montgomery and C. T. Yang (personal communication).
- D. Montgomery and L. Zippin, Topological transformation groups, Interscience, New York, 1964. MR 0073104 (17:383b)
- D. Sullivan, A counterexample to the compact leaf conjecture (to appear).
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