Tischler fibrations of open foliated sets

John Cantwell; Lawrence Conlon

Annales de l'institut Fourier (1981)

  • Volume: 31, Issue: 2, page 113-135
  • ISSN: 0373-0956

Abstract

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Let M be a closed, foliated manifold, and let U be an open, connected, saturated subset that is a union of locally dense leaves without holonomy. Supplementary conditions are given under which U admits an approximating (Tischler) fibration over S 1 . If the fibration exists, conditions under which the original leaves are regular coverings of the fibers are studied also. Examples are given to show that our supplementary conditions are generally required.

How to cite

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Cantwell, John, and Conlon, Lawrence. "Tischler fibrations of open foliated sets." Annales de l'institut Fourier 31.2 (1981): 113-135. <http://eudml.org/doc/74492>.

@article{Cantwell1981,
abstract = {Let $M$ be a closed, foliated manifold, and let $U$ be an open, connected, saturated subset that is a union of locally dense leaves without holonomy. Supplementary conditions are given under which $U$ admits an approximating (Tischler) fibration over $S^1$. If the fibration exists, conditions under which the original leaves are regular coverings of the fibers are studied also. Examples are given to show that our supplementary conditions are generally required.},
author = {Cantwell, John, Conlon, Lawrence},
journal = {Annales de l'institut Fourier},
keywords = {open, connected, saturated subset that is a union of locally dense leaves without holonomy; approximating a foliation by a bundle over the 1-sphere},
language = {eng},
number = {2},
pages = {113-135},
publisher = {Association des Annales de l'Institut Fourier},
title = {Tischler fibrations of open foliated sets},
url = {http://eudml.org/doc/74492},
volume = {31},
year = {1981},
}

TY - JOUR
AU - Cantwell, John
AU - Conlon, Lawrence
TI - Tischler fibrations of open foliated sets
JO - Annales de l'institut Fourier
PY - 1981
PB - Association des Annales de l'Institut Fourier
VL - 31
IS - 2
SP - 113
EP - 135
AB - Let $M$ be a closed, foliated manifold, and let $U$ be an open, connected, saturated subset that is a union of locally dense leaves without holonomy. Supplementary conditions are given under which $U$ admits an approximating (Tischler) fibration over $S^1$. If the fibration exists, conditions under which the original leaves are regular coverings of the fibers are studied also. Examples are given to show that our supplementary conditions are generally required.
LA - eng
KW - open, connected, saturated subset that is a union of locally dense leaves without holonomy; approximating a foliation by a bundle over the 1-sphere
UR - http://eudml.org/doc/74492
ER -

References

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  1. [1] J. CANTWELL and L. CONLON, Nonexponential leaves at finite level, (to appear). Zbl0487.57009
  2. [2] J. CANTWELL and L. CONLON, Poincaré-Bendixson theory for leaves of codimension one, Trans. Amer. Math. Soc. (to appear). Zbl0484.57015
  3. [3] J. CANTWELL and L. CONLON, Growth of leaves, Comm. Math. Helv., 53 (1978), 93-111. Zbl0368.57009MR80b:57021
  4. [4] L. CONLON, Transversally complete e-foliations of codimension two, Trans. Amer. Math. Soc., 194 (1974), 79-102. Zbl0288.57011MR51 #6844
  5. [5] P. DIPPOLITO, Codimension one foliations of closed manifolds, Ann. Math., 107 (1978), 403-453. Zbl0418.57012MR58 #24288
  6. [6] G. DUMINY, (to appear). 
  7. [7] L. FUCHS, Infinite Abelian Groups, Volume I, Academic Press, New York, 1970. Zbl0209.05503MR41 #333
  8. [8] G. HECTOR, Thesis, Strasbourg, 1972. 
  9. [9] H. HOPF, Enden offener Räume und unendliche diskontinuerliche Gruppen, Comm. Math. Helv., 16 (1944), 81-100. Zbl0060.40008MR5,272e
  10. [10] R. SACKSTEDER, Foliations and pseudogroups, Amer. J. Math., 87 (1965), 79-102. Zbl0136.20903MR30 #4268
  11. [11] D. TISCHLER, On fibering certain foliated manifolds over S1, Topology, 9 (1970), 153-154. Zbl0177.52103MR41 #1069
  12. [12] N. TSUCHIYA, Growth and depth of leaves, J. Fac. Sci. Univ. Tokyo, 26 (1979), 473-500. Zbl0448.57009MR81f:57028

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