Speaker: Danica Kosanovic (MPIM Bonn)
Knot invariants from homotopy theory
The embedding calculus of Goodwillie and Weiss is a certain homotopy theoretic technique for studying spaces of embeddings. When applied to the space of knots this method gives a sequence of knot invariants which are conjectured to be universal Vassiliev invariants. This is remarkable since such invariants have been constructed only rationally so far and many questions about possible torsion remain open. In this talk I will present a geometric viewpoint on the embedding calculus, which enables explicit computations. In particular, I will outline a proof that these knot invariants are surjective maps, which confirms part of the conjecture, and indicate how this can be extended to all missing cases in the Goodwillie-Klein connectivity estimates.