TY  - JOUR
ID  - Kowalik2012
LB  - Kowalik2012
AU  - Kowalik, Agnieszka
AU  - Lech, Jacek
AU  - Michalik, Ilona
TI  - On the structure of certain nontransitive diffeomorphism groups on open manifolds
ST  - On the structure of certain nontransitive diffeomorphism groups on open manifolds
JO  - Opuscula Math.
JA  - Opuscula Math.
JF  - Opuscula Mathematica
PY  - 2012
VL  - 32
IS  - 3
SP  - 511
EP  - 520
DO  - http://dx.doi.org/10.7494/OpMath.2012.32.3.511
UR  - http://dx.doi.org/10.7494/OpMath.2012.32.3.511
AB  - 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.
KW  - foliated manifold
KW  - bounded group
KW  - conjugation-invariant norm
KW  - group of diffeomorphisms
KW  - commutator
KW  - perfectness
KW  - uniform perfectness
SN  - 1232-9274
ER  -