On commutators of equivariant homeomorphisms

The long-standing problem of the perfectness of the compactly supported equivariant homeomorphism group on a G-manifold (with one orbit type) is solved in the affirmative. The proof is based on an argument different than that for the case of diffeomorphisms. The theorem is a starting point for computing H 1 ( H G ( M ) ) for more complicated G-manifolds.