Infinite families of links with trivial Jones polynomial

Eliahou, Shalom; Kauffman, Louis H.; Thistlethwaite, Morwen

doi:10.1016/s0040-9383(02)00012-5

Cited by 66 publications

(56 citation statements)

References 11 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…This link, L and the corresponding link L s with a switched crossing have the property that both L and L s have the same Jones polynomial as an unlink of two components. These link diagrams were constructed using the methods of [19].…”

Section: Undetectable Examplesmentioning

confidence: 99%

Minimal surface representations of virtual knots and links

Dye

Kauffman

2005

Algebr. Geom. Topol.

View full text Add to dashboard Cite

Kuperberg [15] has shown that a virtual knot diagram corresponds (up to generalized Reidemeister moves) to a unique embedding in a thickened surface of minimal genus. If a virtual knot diagram is equivalent to a classical knot diagram then this minimal surface is a sphere. Using this result and a generalised bracket polynomial, we develop methods that may determine whether a virtual knot diagram is non-classical (and hence non-trivial). As examples we show that, except for special cases, link diagrams with a single virtualization and link diagrams with a single virtual crossing are non-classical.

show abstract

Section: Undetectable Examplesmentioning

confidence: 99%

Minimal surface representations of virtual knots and links

Dye

Kauffman

2005

Algebr. Geom. Topol.

View full text Add to dashboard Cite

show abstract

“…Note that C is an untwisted double of the core of V 2 . By Propositions 2.3 and 2.4 of [EKT03], L = k ∪ C is a prime link. Let K q denote the knot obtained from k by 1/q-surgery on the trivial knot C. We take q > 0 for simplicity.…”

mentioning

confidence: 96%

Knot Group Epimorphisms

Silver

Whitten

2006

J. Knot Theory Ramifications

View full text Add to dashboard Cite

Let G be a finitely generated group, and let λ ∈ G. If there exists a knot k such that πk = π 1 (S 3 \ k) can be mapped onto G sending the longitude to λ, then there exists infinitely many distinct prime knots with the property. Consequently, if πk is the group of any knot (possibly composite), then there exists an infinite number of prime knots k 1 , k 2 , · · · and epimorphisms · · · → πk 2 → πk 1 → πk each perserving peripheral structures. Properties of a related partial order on knots are discussed.

show abstract

“…In fact, there are certain class of links with trivial Jones' polynomial [28]. We checked some examples of links sharing the same Jones' polynomial but different colored Jones and observed that the Rényi entropies are different.…”

Section: Jhep02(2018)163 5 Conclusion and Discussionmentioning

confidence: 99%

Entanglement on linked boundaries in Chern-Simons theory with generic gauge groups

Dwivedi

Singh

Dhara

et al. 2018

J. High Energ. Phys.

View full text Add to dashboard Cite

We study the entanglement for a state on linked torus boundaries in 3d ChernSimons theory with a generic gauge group and present the asymptotic bounds of Rényi entropy at two different limits: (i) large Chern-Simons coupling k, and (ii) large rank r of the gauge group. These results show that the Rényi entropies cannot diverge faster than ln k and ln r, respectively. We focus on torus links T (2, 2n) with topological linking number n. The Rényi entropy for these links shows a periodic structure in n and vanishes whenever n = 0 (mod p), where the integer p is a function of coupling k and rank r. We highlight that the refined Chern-Simons link invariants can remove such a periodic structure in n.

show abstract

Infinite families of links with trivial Jones polynomial

Abstract: For each k ¿ 2, we exhibit inÿnite families of prime k-component links with Jones polynomial equal to that of the k-component unlink.

Cited by 66 publications

References 11 publications

Minimal surface representations of virtual knots and links

Minimal surface representations of virtual knots and links

Knot Group Epimorphisms

Entanglement on linked boundaries in Chern-Simons theory with generic gauge groups

Contact Info

Product

Resources

About