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

TL;DR

This paper introduces a cellular approximation for the diagonal of multiplihedra, enabling a model for A-infinity morphisms and their tensor products with applications in algebraic and symplectic topology.

Contribution

It provides a new cellular model for the diagonal of multiplihedra and a universal formula for tensor products of A-infinity morphisms, with a compatible operadic bimodule structure.

Findings

Established a cellular approximation for multiplihedra diagonal

Developed a compatible topological operadic bimodule structure

Outlined applications in algebraic and symplectic topology

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.