It is well-known that any isotopically connected diffeomorphism group G of a manifold determines a unique singular foliation . A one-to-one correspondence between the class of singular foliations and a subclass of diffeomorphism groups is established. As an illustration of this correspondence it is shown that the commutator subgroup [G,G] of an isotopically connected, factorizable and non-fixing diffeomorphism group G is simple iff the foliation defined by [G,G] admits no proper minimal sets. In particular, the compactly supported e-component of the leaf preserving diffeomorphism group of a regular foliation ℱ is simple iff ℱ has no proper minimal sets.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-ap103-1-3,
author = {Tomasz Rybicki},
title = {Correspondence between diffeomorphism groups and singular foliations},
journal = {Annales Polonici Mathematici},
volume = {105},
year = {2012},
pages = {27-35},
zbl = {1246.57077},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-ap103-1-3}
}
Tomasz Rybicki. Correspondence between diffeomorphism groups and singular foliations. Annales Polonici Mathematici, Tome 105 (2012) pp. 27-35. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-ap103-1-3/