Annular Links with sl₂-Irreducible Annular Khovanov Homology

Author: Kim, Juhyun

Year: 2021

Degree: Dissertation (Ph.D.)

Advisor: Ni, Yi

Committee Members: Gukov, Sergei; Ni, Yi; Wang, Lu; Chen, Lei

Option: Mathematics

DOI: 10.7907/rwqc-q126

Abstract

We prove that the rank of annular Khovanov homology of a braid in its next-to-top annular grading is always greater than 1, and as an immediate consequence prove that annular Khovanov homology of an annular link as a representation over the Lie algebra sl₂ is irreducible if and only if the annular link is isotopic to the core of the annulus. We also conjecture an analogue of Fox's trapezoid conjecture in the context of annular Khovanov homology with a computer-assisted supporting evidence.

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