Extending regular foliations

J. W. Smith

Annales de l'institut Fourier (1969)

  • Volume: 19, Issue: 2, page 155-168
  • ISSN: 0373-0956

Abstract

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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 F ⊂ F ' . Our main result asserts that if M and F extends over relatively compact subsets of M .

How to cite

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Smith, J. W.. "Extending regular foliations." Annales de l'institut Fourier 19.2 (1969): 155-168. <http://eudml.org/doc/73987>.

@article{Smith1969,
abstract = {A $p$-dimensional foliation $F$ on a differentiable manifold $M$ is said to extend provided there exists a $(p+1)$-dimensional foliation $F^\{\prime \}$ on $M$ with $F\subset F^\{\prime \}$. Our main result asserts that if $M$ and $F$ extends over relatively compact subsets of $M$.},
author = {Smith, J. W.},
journal = {Annales de l'institut Fourier},
keywords = {topology},
language = {eng},
number = {2},
pages = {155-168},
publisher = {Association des Annales de l'Institut Fourier},
title = {Extending regular foliations},
url = {http://eudml.org/doc/73987},
volume = {19},
year = {1969},
}

TY - JOUR
AU - Smith, J. W.
TI - Extending regular foliations
JO - Annales de l'institut Fourier
PY - 1969
PB - Association des Annales de l'Institut Fourier
VL - 19
IS - 2
SP - 155
EP - 168
AB - A $p$-dimensional foliation $F$ on a differentiable manifold $M$ is said to extend provided there exists a $(p+1)$-dimensional foliation $F^{\prime }$ on $M$ with $F\subset F^{\prime }$. Our main result asserts that if $M$ and $F$ extends over relatively compact subsets of $M$.
LA - eng
KW - topology
UR - http://eudml.org/doc/73987
ER -

References

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  1. [EDT] J. R. MUNKRES, Elementary Differential Topology, revised edition, Annals of Math. Study 54, Princeton, N.J., (1966). Zbl0161.20201
  2. [1] C. CHEVALLEY, Theory of Lie Groups, Princeton, (1946). Zbl0063.00842
  3. [2] S. EILENBERG and N. STEENROD, Foundations of Algebraic Topology, Princeton, (1952). Zbl0047.41402MR14,398b
  4. [3] D. HUSEMOLLER, Fibre Bundles, McGraw-Hill, (1966). Zbl0144.44804MR37 #4821
  5. [4] J. W. MILNOR, Lectures on Characteristic Classes, mimeographed notes, Princeton, (1957). 
  6. [5] R. S. PALAIS, A Global Formulation of the Lie Theory of Transformation Groups, Amer. Math. Soc. Memoir 22, (1957). Zbl0178.26502MR22 #12162
  7. [6] J. W. SMITH, The Euler class of generalized vector bundles, Acta Math. 115 (1966), 51-81. Zbl0141.21002MR32 #4704
  8. [7] J. W. SMITH, Submersions of codimension 1, J. of Math. and Mech. 18 (1968), 437-444. Zbl0179.52004MR38 #1689
  9. [8] J. W. SMITH, Commuting vectorfields on open manifolds, Bull. Amer. Math. Soc., 15 (1969), 1013-1016. Zbl0179.52002MR40 #2117
  10. [9] N. STEENROD, The topology of Fibre Bundles, Princeton, (1951). Zbl0054.07103MR12,522b

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