In this short talk, I will introduce the notion of n-morphisms between two A∞-algebras. These higher morphisms are such that 0-morphisms correspond to standard A∞-morphisms and 1-morphisms correspond to A∞-homotopies. Their combinatorics are then encoded by new families of polytopes, which I call the n-multiplihedra and which generalize the standard multiplihedra. Elaborating on works by Abouzaid and Mescher, I will then explain how this higher algebra of A∞-algebras naturally arises in the context of Morse theory, using moduli spaces of perturbed Morse gradient trees.
This video is part of the Institute for Advanced Study‘s Symplectic geometry seminar.
