In this project, we will develop computer code to find the obstructions to the existence of maps between certain topological objects. This is accomplished through an algebraic apparatus known as cohomology. In our situation, we compute cohomology over a finite ring, which makes the problem especially amenable to computer calculation. Bob Bruner has developed a wonderful program to compute certain groups, known as Ext groups, and these are where the obstructions live. The first step of this project will be to determine how many obstructions exist, and then, if possible, figure out a way to eliminate these obstructions.
Abstract algebra, in particular knowledge of rings and groups.