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Annular Links, Double Branched Covers, and Annular Khovanov Homology

[HYBRID WORKSHOP] Floer Homotopical Methods in Low Dimensional and Symplectic Topology November 14, 2022 - November 18, 2022

November 17, 2022 (03:30 PM PST - 04:30 PM PST)
Speaker(s): Gage Martin (Harvard University; Massachusetts Institute of Technology)
Location: SLMath: Eisenbud Auditorium, Online/Virtual
Primary Mathematics Subject Classification No Primary AMS MSC
Secondary Mathematics Subject Classification No Secondary AMS MSC
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Annular Links, Double Branched Covers, And Annular Khovanov Homology

Abstract

Given a link in the thickened annulus, you can construct an associated link in a closed 3-manifold through a double branched cover construction. In this talk we will see that perspective on annular links can be applied to show annular Khovanov homology detects certain braid closures. Unfortunately, this perspective does not capture all information about annular links. We will see a shortcoming of this perspective inspired by the wrapping conjecture of Hoste-Przytycki. This is partially joint work with Fraser Binns.

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Annular Links, Double Branched Covers, And Annular Khovanov Homology

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