GT seminar: "Poincaré duality fibrations and Kontsevich's Lie graph complex"

Abstract: I will talk about certain higher algebraic structure, governed by Kontsevich's Lie graph complex, that can be associated to an oriented
fibration with Poincaré duality fiber. The main construction is a
generalized fiber integration map associated to each Lie graph homology
class and the main result is that this gives a faithful representation
of Lie graph homology. I will discuss how this leads to new possible
interpretations of Lie graph homology classes as obstructions to, on one
hand, smoothness of Poincaré duality fibrations, and, on the other hand,
the existence of Poincaré duality algebra resolutions of the cochains of
the total space as a dg module over the cochains of the base space.

This is a talk in our geometry and topology seminar series.