On the homeomorphism groups of manifolds and their universal coverings

Let 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 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 H _c (M) and its subgroups is investigated. Finally, the structure of the universal covering group of H _c (M) is studied.