On the structure of certain nontransitive diffeomorphism groups on open manifolds

On the structure of certain nontransitive diffeomorphism groups on open manifolds

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 th...

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Bibliographic Details
Main Authors: Agnieszka Kowalik, Jacek Lech, Ilona Michalik
Format: Article
Language:English
Published: AGH Univeristy of Science and Technology Press 2012-01-01
Series:Opuscula Mathematica
Subjects:
foliated manifold
bounded group
conjugation-invariant norm
group of diffeomorphisms
commutator
perfectness
uniform perfectness
Online Access:http://www.opuscula.agh.edu.pl/vol32/3/art/opuscula_math_3235.pdf
Description
Summary: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.
ISSN:1232-9274

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