Abstract
Abstract. The real points of the Deligne—Knudsen—Mumford moduli space \overline \cal M n 0 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.
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