Opuscula Math. 32, no. 3 (2012), 511-520
On the structure of certain nontransitive diffeomorphism groups on open manifolds
Agnieszka Kowalik
Jacek Lech
Ilona Michalik
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.
About the authors ▼
Agnieszka Kowalik
AGH University of Science and Technology, Faculty of Applied Mathematics, al. Mickiewicza 30, 30-059 Krakow, Poland
Jacek Lech
AGH University of Science and Technology, Faculty of Applied Mathematics, al. Mickiewicza 30, 30-059 Krakow, Poland
Ilona Michalik
AGH University of Science and Technology, Faculty of Applied Mathematics, al. Mickiewicza 30, 30-059 Krakow, Poland
About the article ▼
Received: 2011-05-19.
Revised: 2011-09-03.
Accepted: 2011-09-12.
Cite this article as ▼
Agnieszka Kowalik, Jacek Lech, Ilona Michalik, On the structure of certain nontransitive diffeomorphism groups on open manifolds, Opuscula Math. 32, no. 3 (2012), 511-520,
http://dx.doi.org/10.7494/OpMath.2012.32.3.511.
Download this article's citation as: