Homotopy Self-Equivalences of 4-Manifolds

We establish a braid of interlocking exact sequences containing the group of homotopy self-equivalences of a smooth or topological 4-manifold. The braid is computed for manifolds whose fundamental group is finite of odd order. Research partially supported by NSERC Research Grant A4000. The authors thank the Max Planck Institut für Mathematik in Bonn, Germany, for hospitality and support. in final form: 19 November 2003 An erratum to this article is available at.