Knot invariants from homotopy theory
Danica Kosanovic (Paris XIII)
Monday 2nd November, 2020 16:00-17:00 Online
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 some explicit computations and outline why these knot invariants are surjections. This confirms one half of the universality conjecture, and confirms it rationally, and p-adically in a range. We also prove some missing cases of the Goodwillie--Klein connectivity estimates.
The talk will be preceded by a 30 minute tea time. The Zoom link for the seminar is https://uofglasgow.zoom.us/j/91412568415 and the passcode is the genus of the two-dimensional sphere (4 letters, all lowercase).
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