caa a22 4500 445884223 CHVBK 20180317145554.0 cr unu---uuuuu 170323e20110401xx s 000 0 eng 10.1007/s10711-010-9525-4 doi (NATIONALLICENCE)springer-10.1007/s10711-010-9525-4 Rybicki Tomasz Faculty of Applied Mathematics, AGH University of Science and Technology, Al. Mickiewicza 30, 30-059, Kraków, Poland aut Boundedness of certain automorphism groups of an open manifold [Elektronische Daten] [Tomasz Rybicki] 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. Springer Science+Business Media B.V., 2010 Open manifold nationallicence Bounded group nationallicence Conjugation-invariant norm nationallicence Group of diffeomorphisms nationallicence Commutator length nationallicence Perfectness nationallicence Uniform perfectness nationallicence Geometriae Dedicata Springer Netherlands 151/1(2011-04-01), 175-186 0046-5755 151:1<175 2011 151 10711 https://doi.org/10.1007/s10711-010-9525-4 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s10711-010-9525-4 text/html Onlinezugriff via DOI NATIONALLICENCE 100 1- Rybicki Tomasz Faculty of Applied Mathematics, AGH University of Science and Technology, Al. Mickiewicza 30, 30-059, Kraków, Poland aut NATIONALLICENCE 773 0- Geometriae Dedicata Springer Netherlands 151/1(2011-04-01), 175-186 0046-5755 151:1<175 2011 151 10711 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer