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This article is cited in 1 scientific paper (total in 1 paper)
A Cable Knot and BPS-Series
John Chae Department of Mathematics, Univeristy of California Davis, Davis, USA
Abstract:
A series invariant of a complement of a knot was introduced recently. The invariant 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 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.
Keywords:
knot complement, quantum invariant, $q$-series, Chern–Simons theory, categorification.
Received: August 3, 2022; in final form January 5, 2023; Published online January 13, 2023
Citation:
John Chae, “A Cable Knot and BPS-Series”, SIGMA, 19 (2023), 002, 12 pp.
Linking options:
https://www.mathnet.ru/eng/sigma1897 https://www.mathnet.ru/eng/sigma/v19/p2
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Abstract page: | 76 | Full-text PDF : | 13 | References: | 15 |
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