A Cable Knot and BPS-Series
Geometric Topology
2023-01-24 v7 High Energy Physics - Theory
Mathematical Physics
math.MP
Quantum Algebra
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 for finding the former series invariant.
Keywords
Cite
@article{arxiv.2101.11708,
title = {A Cable Knot and BPS-Series},
author = {John Chae},
journal= {arXiv preprint arXiv:2101.11708},
year = {2023}
}