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Commutator subgroups and foliations without holonomy

Author: Tao Li
Journal: Proc. Amer. Math. Soc. 130 (2002), 2471-2477
MSC (2000): Primary 57N10, 57R30
Published electronically: January 23, 2002
MathSciNet review: 1897474
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Abstract: Suppose a manifold $M$ has a codimension one, transversely orientable foliation without holonomy, and $L$ is a leaf. We give a simple, purely topological proof of the theorem that $\pi_1(L)$ is a normal subgroup containing the commutator subgroup of $\pi_1(M)$.

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  • 1. A. Candel and L. Conlon, Foliations. I. Graduate Studies in Mathematics, 23, Amer. Math. Soc., Providence, RI, 2000, pp. 208-211. CMP 2000:06
  • 2. A. Denjoy, Sur les courbes définies par les équations différentielles à la surface du tore, J. Math. Pures Appl. 11 (1932), 333-375.
  • 3. D. Gabai, Foliations and 3-manifolds, Proceedings of the International Congress of Mathematicians, Vol. I, II (Kyoto, 1990), 609-619, Math. Soc. Japan, Tokyo, 1991.MR 93d:57013
  • 4. H. Imanishi, On the theorem of Denjoy-Sacksteder for codimension one foliations without holonomy. J. Math. Kyoto Univ. 14 (1974), 607-634.MR 51:4270
  • 5. T. Li, Laminar branched surfaces in 3-manifolds, Preprint.
  • 6. S. Novikov, Topology of foliations, Trans. Moscow Math. Soc. 14 (1965), 268-305. MR 34:824
  • 7. G. Reeb, Sur la courbure moyenne des variétés intégrales d'une équation de Pfaff $\omega=0$. C. R. Acad. Sci. Paris 231 (1950). 101-102.MR 12:54c
  • 8. H. Rosenberg, Actions of $\mathbb{R}^n$ on manifolds. Comment. Math. Helv. 41 (1966), 170-178. MR 34:6794
  • 9. H. Rosenberg, Foliations by planes. Topology, 7 (1968) 131-138. MR 37:3595
  • 10. R. Sacksteder, Foliations and pseudo-groups, Amer. J. Math. 87 (1965) 79-102.MR 30:4268

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Additional Information

Tao Li
Affiliation: Department of Mathematics, C1200, University of Texas at Austin, Austin, Texas 78712
Address at time of publication: Department of Mathematics, 401 Mathematical Sciences, Oklahoma State University, Stillwater, Oklahoma 74078

Received by editor(s): October 2, 2000
Received by editor(s) in revised form: March 9, 2001
Published electronically: January 23, 2002
Communicated by: Ronald A. Fintushel
Article copyright: © Copyright 2002 American Mathematical Society