The diagonal of the multiplihedra

In-person only.
Contact: Viktoriya Ozornova (viktoriya.ozornova@mpim...)

The structure of homotopy associative algebra, or A-infinity algebra, is encoded by a family of polytopes named associahedra. Morphisms between A-infinity algebras are encoded by another family of polytopes, first introduced by Stasheff: the multiplihedra. In a joint work with Thibaut Mazuir, we define a cellular approximation of the diagonal of the multiplihedra, and describe its image combinatorially. This allows us to define a tensor product of A-infinity morphisms, compatible with that of A-infinity algebras, by explicit formulas. This result opens the doors to explicit computations in symplectic topology, in particular the study of the Fukaya category formed by products of symplectic manifolds