Two-Complexes with Aspherical Fundamental Group.
AMS Contributed Paper Session,
Joint Mathematics Meetings, Atlanta, GA (January 2005).

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, where he constructed homotopy inequivalent 2-complexes one level above the minimal possible Euler characteristic. We take a new look at Dunwoody's work and present generalizations to groups containing the trefoil knot group as a retract.