Foliations with all leaves compact

Epstein, D. B. A.. "Foliations with all leaves compact." Annales de l'institut Fourier 26.1 (1976): 265-282. <http://eudml.org/doc/74269>.

@article{Epstein1976,
abstract = {The notion of the “volume" of a leaf in a foliated space is defined. If $L$ is a compact leaf, then any leaf entering a small neighbourhood of $L$ either has a very large volume, or a volume which is approximatively an integral multiple of the volume of $L$. If all leaves are compact there are three related objects to study. Firstly the topology of the quotient space obtained by identifying each leaf to a point ; secondly the holonomy of a leaf ; and thirdly whether the leaves have a locally bounded volume. We prove various implications relating these concepts and we also give some counterexamples. We give a proof of the result, published by Ehresmann without proof, that in a foliated manifold, if a compact leaf has arbitrarily small neighbourhoods, which are saturated by the leaves, then its holonomy is finite.},
author = {Epstein, D. B. A.},
journal = {Annales de l'institut Fourier},
language = {eng},
number = {1},
pages = {265-282},
publisher = {Association des Annales de l'Institut Fourier},
title = {Foliations with all leaves compact},
url = {http://eudml.org/doc/74269},
volume = {26},
year = {1976},
}

TY - JOUR
AU - Epstein, D. B. A.
TI - Foliations with all leaves compact
JO - Annales de l'institut Fourier
PY - 1976
PB - Association des Annales de l'Institut Fourier
VL - 26
IS - 1
SP - 265
EP - 282
AB - The notion of the “volume" of a leaf in a foliated space is defined. If $L$ is a compact leaf, then any leaf entering a small neighbourhood of $L$ either has a very large volume, or a volume which is approximatively an integral multiple of the volume of $L$. If all leaves are compact there are three related objects to study. Firstly the topology of the quotient space obtained by identifying each leaf to a point ; secondly the holonomy of a leaf ; and thirdly whether the leaves have a locally bounded volume. We prove various implications relating these concepts and we also give some counterexamples. We give a proof of the result, published by Ehresmann without proof, that in a foliated manifold, if a compact leaf has arbitrarily small neighbourhoods, which are saturated by the leaves, then its holonomy is finite.
LA - eng
UR - http://eudml.org/doc/74269
ER -