Joint Topology Seminar

Abstract. Given a knot presented in a grid diagram, we can associate to it a chain complex such that the homology of the chain complex is a powerful invariant called the Heegaard Floer homology. We try to construct a CW complex which has one cell for each generator of the chain complex and whose attaching maps correspond to the chain complex boundary map. Time permitting, we will show that the stable homotopy type of this CW complex is actually a knot invariant.