On the structure of certain nontransitive diffeomorphism groups on open manifolds

Opuscula Mathematica

Agnieszka Kowalik¹  Jacek Lech¹  Ilona Michalik¹ 

[1] AGH University of Science and Technology, Faculty of Applied Mathematics, al. Mickiewicza 30, 30-059 Krakow, Poland;

关键词: foliated manifold;    bounded group;    conjugation-invariant norm;    group of diffeomorphisms;    commutator;    perfectness;    uniform perfectness;   

DOI  :  http://dx.doi.org/10.7494/OpMath.2012.32.3.511

来源: DOAJ

【 摘 要 】

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.

【 授权许可】

Unknown