Add to ORKGA 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.Comment: Clarification adde
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Every two-bridge knot or link is characterized by a rational number p/q, and has a fundamental group...
It has been conjectured that quantum entanglement operators can be lifted to braiding operators by t...
This paper contains the first knot polynomials which can distinguish the orientations of classical k...
We analyze the two variable series invariant for knot complements originating from a categorificatio...
A natural question in knot theory is to ask how certain properties of a knot behave under satellite ...
We prove that the meridional rank and the bridge number of the Whitehead double of a prime algebraic...
The asymptotic expansion of quantum knot invariants in complex Chern-Simons theory gives rise to fac...
Many of the articles in this book are accessible to undergraduates who are working on research or ta...
We discuss relations between quantum BPS invariants defined in terms of a product decomposition of c...
The physical 3d N=2 theory T[Y] was previously used to predict the existence of some 3-manifold inva...
Both the Alexander polynomial and the colored Jones polynomial are well-known knot invariants. While...
This dissertation studies quantum invariants of knots and links, particularly the colored Jones poly...
We automate the process of machine learning correlations between knot invariants. For nearly 200,000...
We study the behavior of the Ozsváth–Szabó and Rasmussen knot concordance invariants τ and s on Km,n...
We show that a topological quantum computer based on the evaluation of a Witten-Reshetikhin-Turaev T...
Every two-bridge knot or link is characterized by a rational number p/q, and has a fundamental group...
It has been conjectured that quantum entanglement operators can be lifted to braiding operators by t...
This paper contains the first knot polynomials which can distinguish the orientations of classical k...