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PQLHT | Melissa Zhang: Lecture 4

Leertaste = Abspielen/Pausieren
m = Stumm
f = Vollbild
Pfeil-links = Zurückspulen
Pfeil-rechts = Vorspulen
Lukas Lewark

PQLHT | Melissa Zhang: Lecture 4

A link L living in a thickened annulus (R^2∖ {0})×[0, 1] is called an annular link. The ambient space equips the bigraded Khovanov chain complex of L with an additional annular (filtration) grading, and the associated graded complex computes the annular Khovanov homology, AKh(L). Understanding annular knots and links is important in many different contexts in low-dimensional topology; this lecture series will survey some existing and potential relationships between AKh and contact topology, knot concordance, representation theory, and more.

Lecture 4: Background on Contact Topology; Plamenevskaya's Transverse Invariant psi from Khovanov homology; Plamenevskaya's psi and the contact invariant c from Heegard Floer; Applications of Grigsby-Licata-Wehrli's annular Rasmussen invariant; Wrapping Conjecture; Crowdsourcing: "How do you think Annular Khovanov homology (and annular theories in general) will be used in the future?"

This lecture was part of the workshop "Perspectives on quantum link homology theories", see https://cbz20.raspberryip.com/Perspectives-2021