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Transactions of the American Mathematical Society

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Transversally parallelizable foliations of codimension two


Author: Lawrence Conlon
Journal: Trans. Amer. Math. Soc. 194 (1974), 79-102
MSC: Primary 57D30
DOI: https://doi.org/10.1090/S0002-9947-1974-0370617-0
Erratum: Trans. Amer. Math. Soc. 207 (1975), 406.
MathSciNet review: 0370617
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Abstract: We study framed foliations such that the framing of the normal bundle can be chosen to be invariant under the linear holonomy of each leaf. In codimension one there is a strong structure theory for such foliations due, e.g., to Novikov, Sacksteder, Rosenberg, Moussu. An analogous theory is developed here for the case of codimension two.


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  • [1] L. V. Ahlfors and L. Sario, Riemann surfaces, Princeton Math. Series, no. 26, Princeton Univ. Press, Princeton, N. J., 1960. MR 22 #5729. MR 0114911 (22:5729)
  • [2] R. Bott, Lectures on characteristic classes and foliations (notes by L. Conlon), Lecture Notes in Math., no. 279, Springer-Verlag, New York, 1972, 1-80. MR 0362335 (50:14777)
  • [3] C. Chevalley, Theory of Lie groups. Vol. I, Princeton Math. Series, vol. 8, Princeton Univ. Press, Princeton, N. J., 1946. MR 7, 412.
  • [4] A. Haefliger, Variétés feuilletées, Ann. Scuola Norm. Sup. Pisa (3) 16 (1962), 367-397. MR 32 #6487. MR 0189060 (32:6487)
  • [5] -, Feuilletages sur les variétés ouvertes, Topology 9 (1970), 183-194. MR 41 #7709. MR 0263104 (41:7709)
  • [6] -, Homotopy and integrability, Manifolds--Amsterdam 1970 (Proc. Nuffic Summer School), Lecture Notes in Math., vol. 197, Springer, Berlin, 1971, pp. 133-163. MR 44 #2251. MR 0285027 (44:2251)
  • [7] S. T. Hu, Homotopy theory, Pure and Appl. Math., vol. 8, Academic Press, New York, 1959. MR 21 #5186. MR 0106454 (21:5186)
  • [8] A. L. Lundell and S. Weingram, The topology of CW complexes, Van Nostrand, New York, 1969.
  • [9] R. Moussu, Feuilletages sans holonomie d'une variété fermée, C. R. Acad. Sci. Paris Sér. A-B 270 (1970), A1308-A1311. MR 41 #7710. MR 0263105 (41:7710)
  • [10] -, Sur un théorème de Novikov, Rev. Colombiana Mat. 3 (1969), 51-81. MR 41 #2703. MR 0258056 (41:2703)
  • [11] R. Moussu and R. Roussarie, Une condition suffisante pour qu'un feuilletage soit sans holonomie, C. R. Acad. Sci. Paris Sér. A-B 271 (1970), A240-A243. MR 43 #2732. MR 0276994 (43:2732)
  • [12] S. P. Novikov, Topology of foliations, Trudy Moskov. Mat. Obšč. 14 (1965), 248-278 = Trans. Moscow Math. Soc. 1965, 268-304. MR 34 #824. MR 0200938 (34:824)
  • [13] J. S. Pasternack, Foliations and compact Lie group actions, Comment. Math. Helv. (1972), 55-65. MR 0300307 (45:9353)
  • [14] B. L. Reinhart, Foliated manifolds with bundle-like mairies, Ann. of Math. (2) 69 (1959), 119-132. MR 21 #6004. MR 0107279 (21:6004)
  • [15] H. Rosenberg, Actions of $ {{\mathbf{R}}^n}$ on manifolds, Comment. Math. Helv. 41 (1966/67), 170-178. MR 34 #6794. MR 0206978 (34:6794)
  • [16] R. Sacksteder, Foliations and pseudogroups, Amer. J. Math. 87 (1965), 79-102. MR 30 #4268. MR 0174061 (30:4268)
  • [17] P. Schweitzer, Counterexamples to the Seifert conjecture and opening closed leaves of foliatons, Ann. of Math. (to appear). MR 0356086 (50:8557)

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DOI: https://doi.org/10.1090/S0002-9947-1974-0370617-0
Article copyright: © Copyright 1974 American Mathematical Society

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