Opuscula Mathematica

Opuscula Math.
, 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.
Cite this article as:
Jacek Lech, On the perfectness of C∞,s-diffeomorphism groups on a foliated manifold, Opuscula Math. 28, no. 3 (2008), 313-324
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ISSN 1232−9274, e-ISSN 2300−6919, DOI https://doi.org/10.7494/OpMath
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