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Topology/Geometry Seminar

Classifying symmetric knots

Keegan Boyle (University of British Columbia)

Location:  Notified via email/contact the organizers
Date & time: Tuesday, 11 April 2023 at 4:00PM - 5:00PM

Abstract:
This talk is about finite group actions on knots. Specifically, I will state a theorem classifying symmetric knots into types, depending on the group action on the 3-sphere and the group action on the image of the knot. This work relies on two key facts: any finite group action on a knot must be cyclic or dihedral, and up to a natural equivalence we can work with subgroups of O(4) instead of subgroups of the diffeomorphism group. The classification then follows from studying orthogonal representations of cyclic and dihedral groups. I will take special care to discuss some of the technical issues involved, including the precise definition of symmetric knot, and the difference between working with oriented and unoriented objects. This is joint work with Nicholas Rouse and Ben Williams.

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