On the Homotopy Classification of 2-Complexes. AMS Special Session on Low-Dimensional Topology II, Joint Mathematics Meetings, Phoenix, AZ (January 2004).

Abstract
The homotopy classification for 2-complexes is complete only when the fundamental group is finite or free. Somewhat isolated is the work of Martin Dunwoody who studied homotopy types of 2-complexes where the fundamental group is the trefoil group. He constructed homotopy inequivalent 2-complexes one level above the minimal possible Euler characteristic (in case of finite of free fundamental groups there is only one homotopy type above the minimal level). We take a new look at Dunwoody's work and present generalizations to other groups of cohomological dimension 2.