On the perfectness of C^{∞,s}-diffeomorphism groups on a foliated manifold

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.

Bibliographic Details
Main Author: Jacek Lech
Format: Article
Language:English
Published: AGH Univeristy of Science and Technology Press 2008-01-01
Series:Opuscula Mathematica
Subjects:
Online Access:http://www.opuscula.agh.edu.pl/vol28/3/art/opuscula_math_2823.pdf