Convex Hull Realizations of the Multiplihedra

Details Convex Hull Realizations of the Multiplihedra Convex Hull Realizations of the Multiplihedra

2007-06-22

arxiv.org/abs/0706.3226v6

Mathematics

Algebraic Topology

typos fixed, introduction revised

Scientific paper

We present a simple algorithm for determining the extremal points in Euclidean space whose convex hull is the nth polytope in the sequence known as the multiplihedra. This answers the open question of whether the multiplihedra could be realized as convex polytopes. We use this realization to unite the approach to A_n-maps of Iwase and Mimura to that of Boardman and Vogt. We include a review of the appearance of the nth multiplihedron for various n in the studies of higher homotopy commutativity, (weak) n-categories, A_infinity-categories, deformation theory, and moduli spaces. We also include suggestions for the use of our realizations in some of these areas as well as in related studies, including enriched category theory and the graph associahedra.

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