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Annular Links with sl₂-Irreducible Annular Khovanov Homology

Citation

Kim, Juhyun (2021) Annular Links with sl₂-Irreducible Annular Khovanov Homology. Dissertation (Ph.D.), California Institute of Technology. doi:10.7907/rwqc-q126. https://resolver.caltech.edu/CaltechTHESIS:05162021-224519644

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.

Item Type:Thesis (Dissertation (Ph.D.))
Subject Keywords:knot theory, annular link, Khovanov homology
Degree Grantor:California Institute of Technology
Division:Physics, Mathematics and Astronomy
Major Option:Mathematics
Thesis Availability:Public (worldwide access)
Research Advisor(s):
  • Ni, Yi
Thesis Committee:
  • Gukov, Sergei (chair)
  • Ni, Yi
  • Wang, Lu
  • Chen, Lei
Defense Date:18 May 2021
Record Number:CaltechTHESIS:05162021-224519644
Persistent URL:https://resolver.caltech.edu/CaltechTHESIS:05162021-224519644
DOI:10.7907/rwqc-q126
ORCID:
AuthorORCID
Kim, Juhyun0000-0002-8447-3758
Default Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:14149
Collection:CaltechTHESIS
Deposited By: Juhyun Kim
Deposited On:27 May 2021 15:36
Last Modified:03 Jun 2021 15:55

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