Correspondence between diffeomorphism groups and singular foliations

• Autorzy: Tomasz Rybicki
• Języki publikacji: EN

Abstrakty

EN

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.

Kategorie tematyczne

• 53C12: Foliations (differential geometric aspects)
• 57R52: Isotopy
• 57R50: Diffeomorphisms

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Annales Polonici Mathematici
• Rocznik: 2012
• Tom: 103
• Numer: 1
• Strony: 27-35

Daty

wydano

2012

Twórcy

autor

Tomasz Rybicki

• Faculty of Applied Mathematics, AGH University of Science and Technology, Al. Mickiewicza 30, 30-059 Kraków, Poland

Identyfikatory

DOI

10.4064/ap103-1-3