THE REGULAR PROJECTIVE SOLUTION SPACE OF THE FIGURE-EIGHT KNOT COMPLEMENT

SABURO MATSUMOTO AND RICHARD RANNARD

Abstract. We define the regular immersed projective solution space for a triangulated 3-manifold, and completely determine it for the figure-8 knot complement. We show that there is a close relationship between vertices of this polytope and normal surfaces of a particularly simple form immersed in the manifold.