Strong Frobenius Algebra Models for Disk-Presheaves

Given a closed manifold, its cohomology carries the structure of a Frobenius algebra. I will explain how such a structure can be lifted to the cochain-level using its configuration spaces of points. Moreover, the construction is invertible, that is, it gives an equivalence between strong Frobenius algebras and Disk-presheaves in commutative algebras. In other words, one can (coherently) recover the cochain algebra of the configuration space of $n$ points on $M$ from the strong Frobenius algebra structure on cochains on $M$.

This talk is based on ongoing joint work with Thomas Willwacher.