Algebra/Topology seminar

Speaker: Florian Naef

Title: Rational Embedding calculus via Frobenius algebras

Abstract: Results of Campos-Willwacher, Idrissi, Willwacher and using results of Lambrechts-Stanley, show that rationally the spaces of configuration of points on a (framed) manifold, seen as a right module over the E_d operad, is the same as a dg Frobenius algebra, at least in the simply connected case. We will see that the same is true without the simply connectedness assumption and in families. More precisely, we will see that the E_d operad is "half Koszul dual" to the involutive (non counital) Frobenius properad. From this we obtain an equivalence between the moduli spaces (or infty-categories) of right E_d modules of configuration space type and involutive Frobenius algebras. Using theory developed by Wahl-Westerland and Klamt we can use this result to interpret/define string topology to be all the operations that exist on the free loop space definable in terms of its configuration spaces.

This is a progress report on joint work with Thomas Willwacher.