Extending regular foliations
Annales de l'Institut Fourier, Volume 19 (1969) no. 2, p. 155-168

A p-dimensional foliation F on a differentiable manifold M is said to extend provided there exists a (p+1)-dimensional foliation F on M with FF . Our main result asserts that if M and F extends over relatively compact subsets of M.

On dit qu’une structure feuilletée F de dimension p sur une variété différentiable M se prolonge s’il existe une structure feuilletée F de dimension p+1 sur M telle que FF . Le résultat principal de cet article est que F se prolonge sur les ensembles relativement compacts de M sous les hypothèses que M et F soient orientables, que F soit propre et que la classe d’Euler de M/F s’annule.

@article{AIF_1969__19_2_155_0,
     author = {Smith, J. W.},
     title = {Extending regular foliations},
     journal = {Annales de l'Institut Fourier},
     publisher = {Imprimerie Durand},
     address = {28 - Luisant},
     volume = {19},
     number = {2},
     year = {1969},
     pages = {155-168},
     doi = {10.5802/aif.325},
     zbl = {0176.21403},
     mrnumber = {42 \#1143},
     language = {en},
     url = {http://www.numdam.org/item/AIF_1969__19_2_155_0}
}
Smith, J. W. Extending regular foliations. Annales de l'Institut Fourier, Volume 19 (1969) no. 2, pp. 155-168. doi : 10.5802/aif.325. http://www.numdam.org/item/AIF_1969__19_2_155_0/

[EDT] J. R. Munkres, Elementary Differential Topology, revised edition, Annals of Math. Study 54, Princeton, N.J., (1966). | Zbl 0161.20201

[1] C. Chevalley, Theory of Lie Groups, Princeton, (1946). | Zbl 0063.00842

[2] S. Eilenberg and N. Steenrod, Foundations of Algebraic Topology, Princeton, (1952). | MR 14,398b | Zbl 0047.41402

[3] D. Husemoller, Fibre Bundles, McGraw-Hill, (1966). | MR 37 #4821 | Zbl 0144.44804

[4] J. W. Milnor, Lectures on Characteristic Classes, mimeographed notes, Princeton, (1957).

[5] R. S. Palais, A Global Formulation of the Lie Theory of Transformation Groups, Amer. Math. Soc. Memoir 22, (1957). | MR 22 #12162 | Zbl 0178.26502

[6] J. W. Smith, The Euler class of generalized vector bundles, Acta Math. 115 (1966), 51-81. | MR 32 #4704 | Zbl 0141.21002

[7] J. W. Smith, Submersions of codimension 1, J. of Math. and Mech. 18 (1968), 437-444. | MR 38 #1689 | Zbl 0179.52004

[8] J. W. Smith, Commuting vectorfields on open manifolds, Bull. Amer. Math. Soc., 15 (1969), 1013-1016. | MR 40 #2117 | Zbl 0179.52002

[9] N. Steenrod, The topology of Fibre Bundles, Princeton, (1951). | MR 12,522b | Zbl 0054.07103