# 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

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topCantwell, 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

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

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