Opuscula Math. 28, no. 3 (2008), 313-324
Opuscula Mathematica
On the perfectness of C∞,s-diffeomorphism groups on a foliated manifold
Abstract. The notion of \(C^{r,s}\) and \(C^{\infty,s}\)-diffeomorphisms is introduced. It is shown that the identity component of the group of leaf preserving \(C^{\infty,s}\)-diffeomorphisms with compact supports is perfect. This result is a modification of the Mather and Epstein perfectness theorem.
Keywords: group of \(C^{\infty}\)-diffeomorphisms, perfectness, commutator, foliation.
Mathematics Subject Classification: 22E65, 57R50.
- Jacek Lech
- AGH University of Science and Technology, Faculty of Applied Mathematics, al. Mickiewicza 30, 30-065 Cracow, Poland
- Received: 2007-11-08.
- Accepted: 2008-04-11.
