Transversally parallelizable foliations of codimension two
HTML articles powered by AMS MathViewer
- by Lawrence Conlon
- Trans. Amer. Math. Soc. 194 (1974), 79-102
- DOI: https://doi.org/10.1090/S0002-9947-1974-0370617-0
- PDF | Request permission
Erratum: Trans. Amer. Math. Soc. 207 (1975), 406.
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.References
- Lars V. Ahlfors and Leo Sario, Riemann surfaces, Princeton Mathematical Series, No. 26, Princeton University Press, Princeton, N.J., 1960. MR 0114911, DOI 10.1515/9781400874538
- Raoul Bott, Lectures on characteristic classes and foliations, Lectures on algebraic and differential topology (Second Latin American School in Math., Mexico City, 1971) Lecture Notes in Math., Vol. 279, Springer, Berlin, 1972, pp. 1–94. Notes by Lawrence Conlon, with two appendices by J. Stasheff. MR 0362335 C. Chevalley, Theory of Lie groups. Vol. I, Princeton Math. Series, vol. 8, Princeton Univ. Press, Princeton, N. J., 1946. MR 7, 412.
- André Haefliger, Variétés feuilletées, Ann. Scuola Norm. Sup. Pisa Cl. Sci. (3) 16 (1962), 367–397 (French). MR 189060
- A. Haefliger, Feuilletages sur les variétés ouvertes, Topology 9 (1970), 183–194 (French). MR 263104, DOI 10.1016/0040-9383(70)90040-6
- André Haefliger, Homotopy and integrability, Manifolds–Amsterdam 1970 (Proc. Nuffic Summer School), Lecture Notes in Mathematics, Vol. 197, Springer, Berlin, 1971, pp. 133–163. MR 0285027
- Sze-tsen Hu, Homotopy theory, Pure and Applied Mathematics, Vol. VIII, Academic Press, New York-London, 1959. MR 0106454 A. L. Lundell and S. Weingram, The topology of CW complexes, Van Nostrand, New York, 1969.
- Robert Moussu, Feuilletage sans holonomie d’une variété fermée, C. R. Acad. Sci. Paris Sér. A-B 270 (1970), A1308–A1311 (French). MR 263105
- Robert Moussu, Sur un théorème de Novikov, Rev. Colombiana Mat. 3 (1969), 51–81 (French). MR 0258056
- Robert Moussu and Robert Roussarie, Une condition suffisante pour qu’un feuilletage soit sans holonomie, C. R. Acad. Sci. Paris Sér. A-B 271 (1970), A240–A243 (French). MR 276994
- S. P. Novikov, The topology of foliations, Trudy Moskov. Mat. Obšč. 14 (1965), 248–278 (Russian). MR 0200938
- J. S. Pasternack, Foliations and compact Lie group actions, Comment. Math. Helv. 46 (1971), 467–477. MR 300307, DOI 10.1007/BF02566859
- Bruce L. Reinhart, Foliated manifolds with bundle-like metrics, Ann. of Math. (2) 69 (1959), 119–132. MR 107279, DOI 10.2307/1970097
- Harold Rosenberg, Actions of $R^{n}$ on manifolds, Comment. Math. Helv. 41 (1966/67), 170–178. MR 206978, DOI 10.1007/BF02566874
- Richard Sacksteder, Foliations and pseudogroups, Amer. J. Math. 87 (1965), 79–102. MR 174061, DOI 10.2307/2373226
- Paul A. Schweitzer, Counterexamples to the Seifert conjecture and opening closed leaves of foliations, Ann. of Math. (2) 100 (1974), 386–400. MR 356086, DOI 10.2307/1971077
Bibliographic Information
- © Copyright 1974 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 194 (1974), 79-102
- MSC: Primary 57D30
- DOI: https://doi.org/10.1090/S0002-9947-1974-0370617-0
- MathSciNet review: 0370617