On the structure of certain nontransitive diffeomorphism groups on open manifolds

Tyt. z nagł.References p. 519.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.Dostępny również w formie drukowanej.KEYWORDS: foliated manifold, bounded group, conjugation-invariant norm, group of diffeomorphisms, commutator, perfectness, uniform perfectness