Generators of Certain Second Homotopy Modules. Colloquium, Texas Christian University, Fort Worth, TX (September 2004).

Abstract

Two-dimensional CW-complexes are an important category of spaces in low-dimensional topology. While the question has been open for many years, classifying these CW-complexes by homotopy type has remained challenging. One method commonly used to attack this classification problem is the use of their second homotopy modules to distinguish their homotopy type. This talk will discuss the problem of classifying finite two-dimensional CW-complexes by focusing on the ability to find generators of their second homotopy modules. Methods will include using "pictures" as well as some more algebraic methods.