Opuscula Math. 28, no. 3 (2008), 313-324
On the perfectness of C<sup>∞,s</sup>-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.
About the authors ▼
Jacek Lech
AGH University of Science and Technology, Faculty of Applied Mathematics, al. Mickiewicza 30, 30-065 Cracow, Poland
About the article ▼
Received: 2007-11-08.
Accepted: 2008-04-11.
Cite this article as ▼
Jacek Lech, On the perfectness of C<sup>∞,s</sup>-diffeomorphism groups on a foliated manifold, Opuscula Math. 28, no. 3 (2008), 313-324,
http://dx.doi.org/10.7494/OpMath.2008.28.3.313.
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