This award is for an REU site for 4 students to take place during the summer of 1988 at Fordham University. The research problem arises in algebraic topology, specifically homotopy theory, a field of pure mathematics usually considered to be well beyond the undergraduate curriculum. This question is within range of undergraduates because it can be reduced to a computer search for certain kinds of matrices. In algebraic topology, questions about a topological space are translated into questions about algebraic objects, usually Abelian groups. These Abelian groups, and homomorphisms between them, can in turn be represented as matrices and matrix operations. This allows for computer representation and manipulation. The undergraduates will design algorithms and implement them on a computer to search for a certain kind of topological object, called a nilpotent complex. By attacking the problem algorithmically, the undergraduates will pioneer a new approach to questions about these spaces. Specifically, the project seeks to answer an unsolved question about the existence of finite three-dimensional nilpotent complexes.
