Opuscula Math. 32, no. 3 (2012), 511-520
On the structure of certain nontransitive diffeomorphism groups on open manifolds
Abstract. 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.
Keywords: foliated manifold, bounded group, conjugation-invariant norm, group of diffeomorphisms, commutator, perfectness, uniform perfectness.
Mathematics Subject Classification: 22E65, 57R30, 57R50, 58B25.
- Received: 2011-05-19.
- Revised: 2011-09-03.
- Accepted: 2011-09-12.