Boundedness of certain automorphism groups of an open manifold

Abstract

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.