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

Abstract : 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-infinity 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.
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Preprints, Working Papers, ...
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https://hal.archives-ouvertes.fr/hal-03737123
Contributor : Guillaume Laplante-Anfossi Connect in order to contact the contributor
Submitted on : Saturday, July 23, 2022 - 12:30:25 PM
Last modification on : Friday, August 5, 2022 - 11:59:59 AM

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  • HAL Id : hal-03737123, version 1
  • ARXIV : 2206.05566

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Guillaume Laplante-Anfossi, Thibaut Mazuir. The diagonal of the multiplihedra and the tensor product of A-infinity morphisms. 2022. ⟨hal-03737123⟩

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