Building Two-Complexes From Group Presentations. Colloquium, Texas State University, San Marcos, TX (January 2005).

Abstract

It is sufficient in the homotopy classification for 2-complexes to consider only 2-complexes built from presentations of groups. This method will be discussed, and what is known about the homotopy classification will be discussed. In particular, the homotopy classification of 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.