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.