Curves on 2-manifolds and isotopies

In 2, 3 R. Baer proved that two homotopie simple closed curves, on an orientable closed 2-manifold M of genus greater than one, are isotopic. He applied this theorem to show that a homeomorphism of M, which is homotopie to the identity, is isotopic to the identity. There have been investigations of the same theorems by W. Brodel 4 and