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.

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Veröffentlicht in:Rocznik Akademii Górniczo-Hutniczej im. Stanisława Staszica. Opuscula Mathematica 2008-01, Vol.28 (3), p.313-324
1. Verfasser: Jacek Lech
Format: Artikel
Sprache:eng
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Zusammenfassung: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.
ISSN:1232-9274