Geometriae Dedicata

, Volume 151, Issue 1, pp 175–186 | Cite as

Boundedness of certain automorphism groups of an open manifold

  • Tomasz Rybicki
Original Paper


It is shown that certain diffeomorphism or homeomorphism groups with no restriction on support of an open manifold (being the interior of a compact manifold) are bounded. It follows that these groups are uniformly perfect. In order to characterize the boundedness several conditions on automorphism groups of an open manifold are introduced. In particular, it is shown that the commutator length diameter of the automorphism group \({\mathcal{D}(M)}\) of a portable manifold M is estimated by 4.


Open manifold Bounded group Conjugation-invariant norm Group of diffeomorphisms Commutator length Perfectness Uniform perfectness 

Mathematics Subject Classification (2000)

22E65 57R50 57S05 


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© Springer Science+Business Media B.V. 2010

Authors and Affiliations

  1. 1.Faculty of Applied MathematicsAGH University of Science and TechnologyKrakówPoland

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