On geometric bases for quantum A-polynomials of knots
Fuente:
arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2024
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| _version_ | 1866913583075426304 |
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| author | Galakhov, Dmitry Morozov, Alexei |
| author_facet | Galakhov, Dmitry Morozov, Alexei |
| contents | A simple geometric way is suggested to derive the Ward identities in the Chern-Simons theory, also known as quantum $A$- and $C$-polynomials for knots. In quasi-classical limit it is closely related to the well publicized augmentation theory and contact geometry. Quantization allows to present it in much simpler terms, what could make these techniques available to a broader audience. To avoid overloading of the presentation, only the case of the colored Jones polynomial for the trefoil knot is considered, though various generalizations are straightforward. Restriction to solely Jones polynomials (rather than full HOMFLY-PT) is related to a serious simplification, provided by the use of Kauffman calculus. Going beyond looks realistic, however it remains a problem, both challenging and promising. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2408_08181 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On geometric bases for quantum A-polynomials of knots Galakhov, Dmitry Morozov, Alexei High Energy Physics - Theory Mathematical Physics Geometric Topology Quantum Algebra A simple geometric way is suggested to derive the Ward identities in the Chern-Simons theory, also known as quantum $A$- and $C$-polynomials for knots. In quasi-classical limit it is closely related to the well publicized augmentation theory and contact geometry. Quantization allows to present it in much simpler terms, what could make these techniques available to a broader audience. To avoid overloading of the presentation, only the case of the colored Jones polynomial for the trefoil knot is considered, though various generalizations are straightforward. Restriction to solely Jones polynomials (rather than full HOMFLY-PT) is related to a serious simplification, provided by the use of Kauffman calculus. Going beyond looks realistic, however it remains a problem, both challenging and promising. |
| title | On geometric bases for quantum A-polynomials of knots |
| topic | High Energy Physics - Theory Mathematical Physics Geometric Topology Quantum Algebra |
| url | https://arxiv.org/abs/2408.08181 |