Strong topological rigidity of noncompact orientable surfaces

Strong topological rigidity of noncompact orientable surfaces SUMANTA DASWe show that every orientable infinite-type surface is properly rigid as a consequence of a more general result.Namely, we prove that if a homotopy equivalence between any two noncompact orientable surfaces is a proper map, then it is properly homotopic to a homeomorphism, provided the surfaces are neither the plane nor the punctured plane.Thus all noncompact orientable surfaces, except the plane and the punctured plane, are topologically rigid in a strong sense.