Opuscula Math.
28
, no. 3
(), 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.