Correspondence between diffeomorphism groups and singular foliations

Tomasz Rybicki. "Correspondence between diffeomorphism groups and singular foliations." Annales Polonici Mathematici 103.1 (2012): 27-35. <http://eudml.org/doc/280993>.

@article{TomaszRybicki2012,
abstract = {It is well-known that any isotopically connected diffeomorphism group G of a manifold determines a unique singular foliation $ℱ_G$. 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 $C^r$ diffeomorphism group G is simple iff the foliation $ℱ_\{[G,G]\}$ defined by [G,G] admits no proper minimal sets. In particular, the compactly supported e-component of the leaf preserving $C^\{∞\}$ diffeomorphism group of a regular foliation ℱ is simple iff ℱ has no proper minimal sets.},
author = {Tomasz Rybicki},
journal = {Annales Polonici Mathematici},
keywords = {diffeomorphism group; singular foliation; commutator group; simple group; leaf preserving diffeomorphism},
language = {eng},
number = {1},
pages = {27-35},
title = {Correspondence between diffeomorphism groups and singular foliations},
url = {http://eudml.org/doc/280993},
volume = {103},
year = {2012},
}

TY - JOUR
AU - Tomasz Rybicki
TI - Correspondence between diffeomorphism groups and singular foliations
JO - Annales Polonici Mathematici
PY - 2012
VL - 103
IS - 1
SP - 27
EP - 35
AB - It is well-known that any isotopically connected diffeomorphism group G of a manifold determines a unique singular foliation $ℱ_G$. 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 $C^r$ diffeomorphism group G is simple iff the foliation $ℱ_{[G,G]}$ defined by [G,G] admits no proper minimal sets. In particular, the compactly supported e-component of the leaf preserving $C^{∞}$ diffeomorphism group of a regular foliation ℱ is simple iff ℱ has no proper minimal sets.
LA - eng
KW - diffeomorphism group; singular foliation; commutator group; simple group; leaf preserving diffeomorphism
UR - http://eudml.org/doc/280993
ER -