Topological Quantum Field Theory Seminar   RSS

Danica Kosanović 29/05/2020, 17:00 — 18:00 — Online
, Max-Planck Institut für Mathematik

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, we prove that these knot invariants are surjective maps, confirming a part of the universality conjecture, and we also confirm the full conjecture rationally, using some recent results in the field. Hence, these invariants are at least as good as configuration space integrals.

See also

Slides of the talk

Projecto FCT UIDB/04459/2020.

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Current organizers: Roger Picken, John Huerta, Marko Stošić.


FCT Projects PTDC/MAT-GEO/3319/2014, Quantization and Kähler Geometry, PTDC/MAT-PUR/31089/2017, Higher Structures and Applications.