Homotopy types of homeomorphism groups of noncompact 2-manifolds

AbstractSuppose M is a noncompact connected PL 2-manifold and let H(M)0 denote the identity component of the homeomorphism group of M with the compact-open topology. In this paper we classify the homotopy type of H(M)0 by showing that H(M)0 has the homotopy type of the circle if M is the plane, an open or half open annulus, or the punctured projective plane. In all other cases we show that H(M)0 is homotopically trivial