The diagonal of the multiplihedra and the tensor product of \(\mathrm{A}_\infty\)-morphisms. (La diagonale des multiplièdres et le produit tensoriel de morphismes \(\mathrm{A}_\infty\).) (English. French summary) Zbl 1516.52011
Summary: We define a cellular approximation for the diagonal of the Forcey-Loday realizations of the multiplihedra, and endow them with a compatible topological cellular operadic bimodule structure over the Loday realizations of the associahedra. This provides us with a model for topological and algebraic \(\mathrm{A}_\infty\)-morphisms, as well as a universal and explicit formula for their tensor product. We study the monoidal properties of this newly defined tensor product and conclude by outlining several applications, notably in algebraic and symplectic topology.
MSC:
| 52B05 | Combinatorial properties of polytopes and polyhedra (number of faces, shortest paths, etc.) |
| 18M70 | Algebraic operads, cooperads, and Koszul duality |
Keywords:
multiplihedra; approximation of diagonal; associahedra; operads; tensor product; A-infinity algebras; S-infinity morphisms; S-infinity categoriesSoftware:
OEISReferences:
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