A Magnus Embedding Theorem for Second Homotopy Modules. Texas NExT Research Session, Meeting of the Texas Section of the MAA, Huntsville, TX (April 2003).
Abstract
An open question in low dimensional topology is the classification of the homotopy type of 2-dimensional CW-complexes. We will examine this question and survey known results, focusing on a result of Dunwoody, et al. (1970s). We will then give an extension of Dunwoody's approach by generalizing the Magnus Embedding Theorem to second homotopy modules. We will provide sample calculations of generating sets of second homotopy modules for some specific groups using this new approach.