Abstract: It has been known since the 1930s that two finite2-dimensional CW-complexes with the same fundamental group and Euler characteristic become homotopy equivalent after wedging with a number of copies of S^2. However, it took until the 1970s to find examples which were not themselves homotopy equivalent. A long-standing problem has since been to determine for which k there exists examples with Euler characteristic k above the minimal value for a fixed fundamental group G. In the first part of this talk, I will discuss my complete resolution to this problem using techniques from integral representation theory.
A large part of the motivation for this work is a close analogy between the homotopy type of a finite 2-complex and the homeomorphism type of a smooth closed 4-manifold. I will explain this analogy and then discuss one aspect of the classification of 4-manifolds on which I hope my work on 2-complexes will eventually have an impact.
Zoom Id: https://iu.zoom.us/j/88198565168
