Knot Complement, ADO Invariants and their Deformations for Torus Knots
A relation between the two-variable series knot invariant and the Akutsu-Deguchi-Ohtsuki (ADO) invariant was conjectured recently. We reinforce the conjecture by presenting explicit formulas and/or an algorithm for particular ADO invariants of torus knots obtained from the series invariant of the co...
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| Опубліковано в: : | Symmetry, Integrability and Geometry: Methods and Applications |
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| Дата: | 2020 |
| Автор: | |
| Формат: | Стаття |
| Мова: | Англійська |
| Опубліковано: |
Інститут математики НАН України
2020
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| Онлайн доступ: | https://nasplib.isofts.kiev.ua/handle/123456789/211085 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Цитувати: | Knot Complement, ADO Invariants and their Deformations for Torus Knots. John Chae. SIGMA 16 (2020), 134, 16 pages |
Репозитарії
Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862635133417291776 |
|---|---|
| author | Chae, John |
| author_facet | Chae, John |
| citation_txt | Knot Complement, ADO Invariants and their Deformations for Torus Knots. John Chae. SIGMA 16 (2020), 134, 16 pages |
| collection | DSpace DC |
| container_title | Symmetry, Integrability and Geometry: Methods and Applications |
| description | A relation between the two-variable series knot invariant and the Akutsu-Deguchi-Ohtsuki (ADO) invariant was conjectured recently. We reinforce the conjecture by presenting explicit formulas and/or an algorithm for particular ADO invariants of torus knots obtained from the series invariant of the complement of a knot. Furthermore, one parameter deformation of the ADO₃ polynomial of torus knots is provided.
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| first_indexed | 2026-03-14T22:43:42Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-211085 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2026-03-14T22:43:42Z |
| publishDate | 2020 |
| publisher | Інститут математики НАН України |
| record_format | dspace |
| spelling | Chae, John 2025-12-23T13:12:12Z 2020 Knot Complement, ADO Invariants and their Deformations for Torus Knots. John Chae. SIGMA 16 (2020), 134, 16 pages 1815-0659 2020 Mathematics Subject Classification: 57K14; 57K16; 81R50 arXiv:2007.13277 https://nasplib.isofts.kiev.ua/handle/123456789/211085 https://doi.org/10.3842/SIGMA.2020.134 A relation between the two-variable series knot invariant and the Akutsu-Deguchi-Ohtsuki (ADO) invariant was conjectured recently. We reinforce the conjecture by presenting explicit formulas and/or an algorithm for particular ADO invariants of torus knots obtained from the series invariant of the complement of a knot. Furthermore, one parameter deformation of the ADO₃ polynomial of torus knots is provided. I am grateful to Sergei Gukov for his valuable suggestions on a draft of this paper. I would like thank Angus Gruen for helpful conversations. I am also grateful to the referees for many helpful suggestions. en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications Knot Complement, ADO Invariants and their Deformations for Torus Knots Article published earlier |
| spellingShingle | Knot Complement, ADO Invariants and their Deformations for Torus Knots Chae, John |
| title | Knot Complement, ADO Invariants and their Deformations for Torus Knots |
| title_full | Knot Complement, ADO Invariants and their Deformations for Torus Knots |
| title_fullStr | Knot Complement, ADO Invariants and their Deformations for Torus Knots |
| title_full_unstemmed | Knot Complement, ADO Invariants and their Deformations for Torus Knots |
| title_short | Knot Complement, ADO Invariants and their Deformations for Torus Knots |
| title_sort | knot complement, ado invariants and their deformations for torus knots |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/211085 |
| work_keys_str_mv | AT chaejohn knotcomplementadoinvariantsandtheirdeformationsfortorusknots |