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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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
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spelling doaj-c8f90ced0365471a94109aff6ca07edc2020-11-24T23:50:17ZengAGH Univeristy of Science and Technology PressOpuscula Mathematica1232-92742012-01-01323511520http://dx.doi.org/10.7494/OpMath.2012.32.3.5113235On the structure of certain nontransitive diffeomorphism groups on open manifoldsAgnieszka Kowalik0Jacek Lech1Ilona Michalik2AGH University of Science and Technology, Faculty of Applied Mathematics, al. Mickiewicza 30, 30-059 Krakow, PolandAGH University of Science and Technology, Faculty of Applied Mathematics, al. Mickiewicza 30, 30-059 Krakow, PolandAGH University of Science and Technology, Faculty of Applied Mathematics, al. Mickiewicza 30, 30-059 Krakow, PolandIt 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.http://www.opuscula.agh.edu.pl/vol32/3/art/opuscula_math_3235.pdffoliated manifoldbounded groupconjugation-invariant normgroup of diffeomorphismscommutatorperfectnessuniform perfectness
collection DOAJ
language English
format Article
sources DOAJ
author Agnieszka Kowalik
Jacek Lech
Ilona Michalik
spellingShingle Agnieszka Kowalik
Jacek Lech
Ilona Michalik
On the structure of certain nontransitive diffeomorphism groups on open manifolds
Opuscula Mathematica
foliated manifold
bounded group
conjugation-invariant norm
group of diffeomorphisms
commutator
perfectness
uniform perfectness
author_facet Agnieszka Kowalik
Jacek Lech
Ilona Michalik
author_sort Agnieszka Kowalik
title On the structure of certain nontransitive diffeomorphism groups on open manifolds
title_short On the structure of certain nontransitive diffeomorphism groups on open manifolds
title_full On the structure of certain nontransitive diffeomorphism groups on open manifolds
title_fullStr On the structure of certain nontransitive diffeomorphism groups on open manifolds
title_full_unstemmed On the structure of certain nontransitive diffeomorphism groups on open manifolds
title_sort on the structure of certain nontransitive diffeomorphism groups on open manifolds
publisher AGH Univeristy of Science and Technology Press
series Opuscula Mathematica
issn 1232-9274
publishDate 2012-01-01
description 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.
topic foliated manifold
bounded group
conjugation-invariant norm
group of diffeomorphisms
commutator
perfectness
uniform perfectness
url http://www.opuscula.agh.edu.pl/vol32/3/art/opuscula_math_3235.pdf
work_keys_str_mv AT agnieszkakowalik onthestructureofcertainnontransitivediffeomorphismgroupsonopenmanifolds
AT jaceklech onthestructureofcertainnontransitivediffeomorphismgroupsonopenmanifolds
AT ilonamichalik onthestructureofcertainnontransitivediffeomorphismgroupsonopenmanifolds
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