Algebra/Topology Seminar

Speaker: Alexander Berglund

Title: Poincaré duality fibrations and graph complexes

Abstract: I will discuss certain higher algebraic structure, governed by Kontsevich's Lie graph complex, that can be associated to an oriented fibration with Poincaré duality fiber. The talk will focus on open problems this raises. These problems are related to, on one hand, the classical problem in commutative algebra about the existence of multiplicative structures on minimal free resolutions and, on the other hand, the question of whether a given Poincaré duality fibration underlies a smooth manifold bundle.