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## Annales Polonici Mathematici

2012 | 103 | 1 | 27-35
Tytuł artykułu

### Correspondence between diffeomorphism groups and singular foliations

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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.
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Tom
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27-35
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wydano
2012
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• Faculty of Applied Mathematics, AGH University of Science and Technology, Al. Mickiewicza 30, 30-059 Kraków, Poland
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