On the Homotopy Type of Two-Complexes with Aspherical Fundamental Group.
Special Session on Geometric Topology and Group Theory,
Meeting of the Southeast Session of the AMS, Bowling Green, KY (March 2005).

Abstract
This talk is concerned with the homotopy classification of finite CW-complexes. A (G,n)-complex is a finite n-dimensional CW-complex with fundamental group G and vanishing higher homotopy groups up to dimension n-1. In case G is finite dimensional, there is a unique (up to homotopy) (G,n)-complex on the minimal Euler characteristic level. We show that if the finite dimensional group G contains the trefoil group T as a retract then there is more than on homotopy type on level one above minimal Euler characteristic.