On the structure of certain nontransitive diffeomorphism groups on open manifolds

Agnieszka Kowalik, Jacek Lech, Ilona Michalik
2012 Opuscula Mathematica  
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.
doi:10.7494/opmath.2012.32.3.511 fatcat:uijd3ddwe5h3llfxw4xkjdx74u