A New Magnus Embedding Theorem. Joint Mathematics Meetings, Baltimore, MD (January 2003).

Abstract

An open question in low dimensional topology is the classification of the homotopy type of two-complexes. One tool in this pursuit is the 1939 Magnus Embedding Theorem, a method of embedding the relation module into a certain matrix group. This result aided Dunwoody's discovery of two distinct homotopy types at a non-minimal level for two-complexes built from presentations of the trefoil knot group. We extend the Magnus embedding theorem to an embedding for $\pi_2$ as a means of extending Dunwoody's results.