A Space of Cyclohedra

Abstract. The real points of the Deligne—Knudsen—Mumford moduli space \overline \cal M n0 of marked points on the sphere have a natural tiling by associahedra. We extend this idea to construct an aspherical space tiled by cyclohedra . We explore the structure of this space, coming from blow-ups of hyperplane arrangements, as well as discuss possibilities of its role in knot theory and mathematical physics.