Browsing by Subject "perfectness"

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Access status: Open Access ,
On the perfectness of C∞,s-diffeomorphism groups on a foliated manifold
(2008) Lech, Jacek
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.
Access status: Open Access ,
On the structure of certain nontransitive diffeomorphism groups on open manifolds
(2012) Kowalik, Agnieszka; Lech, Jacek; Michalik, Ilona
It is shown that in some generic cases the identity component of the group of leaf preserving diffeomorphisms (with not necessarily compact support) on a foliated open manifold is perfect. Next, it is proved that it is also bounded, i.e. bounded with respect to any bi-invariant metric. It follows that the group is uniformly perfect as well.