Knotted families of arcs

Abstract: Goodwillie and Weiss developed a powerful homotopy theoretic technique for studying spaces of embeddings. For properly embedded arcs in a manifold of any dimension these techniques can be given a geometric flavour inspired by Vassiliev theory for classical knots. The outcome is a set of explicit nontrivial classes in homotopy groups of spaces of arcs. I will give an overview of this story, and also outline how such computations can be applied to some open problems in 4-dimensional topology. The latter is joint work with Peter Teichner.

Mathematics

Audience: researchers in the topic

MIT Geometry and Topology Seminar

Series comments: Password is "topology".