QM Research Seminar: A-infinity algebras and homotopy groups of spheres

Speaker: Guillaume Laplante-Anfossi (University of Southern Denmark)
Abstract:
The goal of this talk is to describe a strategy to compute algorithmically unstable homotopy groups of spheres modulo a prime number, using the theory of A-infinity algebras. This approach, which is based on Brown's theory of twisting cochains and its generalisation to A-infinity algebras by Kadeishvili, was proposed by Alain Prouté in 1986. One central ingredient that was missing at the time is a formula for the tensor product of A-infinity algebras and A-infinity morphisms, which are now available and were studied recently in combinatorics. In fact, these techniques can be used more generally to compute the homology of fibered spaces, and could potentially be used to develop a theory of Sullivan minimal models in characteristic p.