Opuscula Math. 28, no. 3 (2008), 313-324

Opuscula Mathematica

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

Jacek Lech

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.

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• Jacek Lech
• AGH University of Science and Technology, Faculty of Applied Mathematics, al. Mickiewicza 30, 30-065 Cracow, Poland