On the Homotopy Classification of 2-Complexes. Topology Seminar, Rice University, Houston, TX (March 2004).

Abstract

A way of distinguishing the homotopy type of connected two-dimensional CW-complexes is by examining their second homotopy module. To determine the homotopy type of two-dimensional CW-complexes, one can restrict their attention to two-dimensinal CW-complexes built from the presentation of the group. A very visual way to examine the second homotoy module of these spaces is to examine pictures over the presentation. We examine pictures and discuss results on the homotopy classification of two-dimensional CW-complexes.