QM Research Seminar: Dioperadic Koszulity and Poincaré duality

Speaker: Alex Takeda (Uppsala University)
Abstract:
In rational homotopy theory, there are notions of formality and coformality of a topological space, related to how “simple” the higher structures on their minimal models are. In particular, for simply connected spaces, the notion of coformality, which measures how simple is the Quillen model for its rational homotopy groups, can be related to the formality of A-infinity algebras, which is something that can be stated entirely within the homotopy theory of operadic algebras. In this talk I will explain a generalization of this latter notion of formality that extends this notion to a pair (X,[X]) of a space with a fundamental class giving local Poincaré duality. This is phrased in terms of algebras over a certain dioperad Y, which one can show is Koszul using a certain geometric construction. Part of this talk is about joint work with C. Emprin.