A Khovanov Laplacian and Khovanov Dirac for Knots and Links
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866913611376492544 |
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| author | Jones, Benjamin Wei, Guo-Wei |
| author_facet | Jones, Benjamin Wei, Guo-Wei |
| contents | Khovanov homology has been the subject of much study in knot theory and low dimensional topology since 2000. This work introduces a Khovanov Laplacian and a Khovanov Dirac to study knot and link diagrams. The harmonic spectrum of the Khovanov Laplacian or the Khovanov Dirac retains the topological invariants of Khovanov homology, while their non-harmonic spectra reveal additional information that is distinct from Khovanov homology. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2411_18841 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | A Khovanov Laplacian and Khovanov Dirac for Knots and Links Jones, Benjamin Wei, Guo-Wei Geometric Topology Algebraic Topology Khovanov homology has been the subject of much study in knot theory and low dimensional topology since 2000. This work introduces a Khovanov Laplacian and a Khovanov Dirac to study knot and link diagrams. The harmonic spectrum of the Khovanov Laplacian or the Khovanov Dirac retains the topological invariants of Khovanov homology, while their non-harmonic spectra reveal additional information that is distinct from Khovanov homology. |
| title | A Khovanov Laplacian and Khovanov Dirac for Knots and Links |
| topic | Geometric Topology Algebraic Topology |
| url | https://arxiv.org/abs/2411.18841 |