Boundedness of certain automorphism groups of an open manifold

Details Boundedness of certain automorphism groups of an open manifold Boundedness of certain automorphism groups of an open manifold

2009-12-23

arxiv.org/abs/0912.4590v4

Geom. Dedicata 151(2011), 175-186

Mathematics

Differential Geometry

revised version

Scientific paper

It is shown that certain diffeomorphism or homeomorphism groups with no restriction on support of an open manifold with finite number of ends 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 $2fragd_{\mathcal D(M)}+2$, where $fragd_{\mathcal D(M)}$ is the diameter of $\mathcal D(M)$ in the fragmentation norm.

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