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On the structure of certain nontransitive diffeomorphism groups on open manifolds

Kowalik A., Lech J., Michalik I.

Opuscula Mathematica

2012

Vol. 32, no. 3

511-520

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.