Cellular chains on freehedra and operadic pairs

Poliakova, Daria

doi:10.48550/arxiv.2011.11607

Cited by 1 publication

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“…The preceding two properties are in fact always satisfied up to homotopy (see Proposition 4.26), which points towards the idea that the category ∞-A ∞ -alg should possess some kind of homotopy symmetric monoidal structure. An analogous phenomenon was already observed for the category of homotopy representations of an algebraic group [AACD11,Pol20].…”

Section: Introductionsupporting

confidence: 74%

The diagonal of the multiplihedra and the tensor product of A ∞ -morphisms

Laplante-Anfossi¹,

Mazuir²

2023

Journal De L’École Polytechnique — Mathématiques

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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 A∞-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. Résumé (La diagonale des multiplièdres et le produit tensoriel de morphismes A-infini)On définit une approximation cellulaire de la diagonale des réalisations de Forcey-Loday des multiplièdres, et on les munit d'une structure de bimodule opéradique topologique et cellulaire compatible sur les réalisations de Loday des associaèdres. On obtient ainsi un modèle algébrique et topologique pour les morphismes A-infini, de même qu'une formule universelle explicite pour leur produit tensoriel. On étudie la monoïdalité de ce nouveau produit tensoriel et on conclut en esquissant plusieurs applications en topologie algébrique et en topologie symplectique.

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Section: Introductionsupporting

confidence: 74%