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.