On the homeomorphism groups of manifolds and their universal coverings

Details On the homeomorphism groups of manifolds and their universal coverings On the homeomorphism groups of manifolds and their universal coverings

2011-04-12

arxiv.org/abs/1104.2227v3

Mathematics

Differential Geometry

19 pages

Scientific paper

Let $\mathcal H_c(M)$ stand for the path connected identity component of the group of all compactly supported homeomorphisms of a manifold $M$. It is shown that $\mathcal H_c(M)$ is perfect and simple under mild assumptions on $M$. Next, conjugation-invariant norms on $\H_c(M)$ are considered and the boundedness of $\mathcal H_c(M)$ is investigated. Finally, the structure of the universal covering group of $\mathcal H_c(M)$ is studied.

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