The diagonal of the operahedra. (English) Zbl 1498.52021
The paper introduces a general theory of coherent cellular approximations of the diagonal for families of polytopes. The results are applied to various classes of polytopes including associahedra and permutahedra. Compatible topological cellular operad structure on the Loday realizations of the operahedra is obtained providing a model for topological and algebraic homotopy operads and an explicit functorial formula for their tensor product. The fundamental hyperplane arrangement of a polytope plays an important role in the considerations.
Reviewer: Andriy Prymak (Winnipeg)
MSC:
| 52B11 | \(n\)-dimensional polytopes |
| 52C35 | Arrangements of points, flats, hyperplanes (aspects of discrete geometry) |
| 52A27 | Approximation by convex sets |
| 18M70 | Algebraic operads, cooperads, and Koszul duality |
Keywords:
polytopes; approximation of the diagonal; operads; hyperplane arrangements; fiber polytopes; generalized permutahedraReferences:
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