A Cable Knot and BPS-Series
A series invariant of the complement of a knot was introduced recently. The invariants for several prime knots up to ten crossings have been explicitly computed. We present the first example of a satellite knot, namely, a cable of the figure eight knot, which has more than ten crossings. This cable...
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| Опубліковано в: : | Symmetry, Integrability and Geometry: Methods and Applications |
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| Дата: | 2023 |
| Автор: | |
| Формат: | Стаття |
| Мова: | Англійська |
| Опубліковано: |
Інститут математики НАН України
2023
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| Онлайн доступ: | https://nasplib.isofts.kiev.ua/handle/123456789/211882 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Цитувати: | A Cable Knot and BPS-Series. John Chae. SIGMA 19 (2023), 002, 12 pages |
Репозитарії
Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862539035579252736 |
|---|---|
| author | Chae, John |
| author_facet | Chae, John |
| citation_txt | A Cable Knot and BPS-Series. John Chae. SIGMA 19 (2023), 002, 12 pages |
| collection | DSpace DC |
| container_title | Symmetry, Integrability and Geometry: Methods and Applications |
| description | A series invariant of the complement of a knot was introduced recently. The invariants for several prime knots up to ten crossings have been explicitly computed. We present the first example of a satellite knot, namely, a cable of the figure eight knot, which has more than ten crossings. This cable knot result provides nontrivial evidence for the conjectures for the series invariant and demonstrates the robustness of the integrality of the quantum invariant under the cabling operation. Furthermore, we observe a relation between the series invariant of the cable knot and the series invariant of the figure eight knot. This relation provides an alternative, simple method of finding the former series invariant.
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| first_indexed | 2026-03-12T18:56:37Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-211882 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2026-03-12T18:56:37Z |
| publishDate | 2023 |
| publisher | Інститут математики НАН України |
| record_format | dspace |
| spelling | Chae, John 2026-01-14T09:56:54Z 2023 A Cable Knot and BPS-Series. John Chae. SIGMA 19 (2023), 002, 12 pages 1815-0659 2020 Mathematics Subject Classification: 57K10; 57K16; 57K31; 81R50 arXiv:2101.11708 https://nasplib.isofts.kiev.ua/handle/123456789/211882 https://doi.org/10.3842/SIGMA.2023.002 A series invariant of the complement of a knot was introduced recently. The invariants for several prime knots up to ten crossings have been explicitly computed. We present the first example of a satellite knot, namely, a cable of the figure eight knot, which has more than ten crossings. This cable knot result provides nontrivial evidence for the conjectures for the series invariant and demonstrates the robustness of the integrality of the quantum invariant under the cabling operation. Furthermore, we observe a relation between the series invariant of the cable knot and the series invariant of the figure eight knot. This relation provides an alternative, simple method of finding the former series invariant. I would like to thank Sergei Gukov, Thang Lê, and Laura Starkston for helpful conversations. I am grateful to Ciprian Manolescu for valuable suggestions on a draft of this paper. I am also grateful to Colin Adams for valuable comments. I would like to thank the referees for the suggestions that led to an improvement of my manuscript. en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications A Cable Knot and BPS-Series Article published earlier |
| spellingShingle | A Cable Knot and BPS-Series Chae, John |
| title | A Cable Knot and BPS-Series |
| title_full | A Cable Knot and BPS-Series |
| title_fullStr | A Cable Knot and BPS-Series |
| title_full_unstemmed | A Cable Knot and BPS-Series |
| title_short | A Cable Knot and BPS-Series |
| title_sort | cable knot and bps-series |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/211882 |
| work_keys_str_mv | AT chaejohn acableknotandbpsseries AT chaejohn cableknotandbpsseries |