Convex Hull Realizations of the Multiplihedra
By Stefan Forcey. 2007
61 citations recorded by the source corpus.
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.
View Paper: https://www.semanticscholar.org/paper/688aa33c11b8baef6f55ad70f771738bf05a3771
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Citations in the corpus
- Geometric realizations of the multiplihedra (2010, methodology): “In particular, Mn,1 is isomorphic as a CW-complex to a convex polytope; this reproduces the result of Forcey [ 2 ].”