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.)) | ||||
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| 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): |
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| Thesis Committee: |
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| 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: |
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| 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: | 05 Jul 2022 19:01 |
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