## 1,277 Citations

An oriented state model for the Jones polynomial and its applications alternating links

- MathematicsAppl. Math. Comput.
- 2007

Jones and $Q$ polynomials for $2$-bridge knots and links

- Mathematics
- 1990

It is known that the Q polynomial of a 2-bridge knot or link can be obtained from the Jones polynomial. We construct arbitrarily many 2-bridge knots or links with the same Q polynomial but distinct…

ORIENTED STATE MODEL OF THE JONES POLYNOMIAL AND ITS CONNECTION TO THE DICHROMATIC POLYNOMIAL

- Computer Science
- 2010

This paper succeeds in adding the writhe to the state sum model and need not to compute the writher any more, and shows that Jones polynomial of any link (alternating or not) is a special parametrization of the dichromatic polynometric of a weighted graph with two different edge weights.

A link polynomial via a vertex-edge-face state model

- Mathematics
- 2007

AbstractWe construct a 2-variable link polynomial, called W L , for classicallinks by considering simultaneously the Kauﬀman state models forthe Alexander and for the Jones polynomials. We conjecture…

The Colored Jones Polynomial and the A-Polynomial of Two-Bridge Knots

- Mathematics
- 2004

We study relationships between the colored Jones polynomial and the A-polynomial of a knot. We establish for a large class of 2-bridge knots the AJ conjecture (of Garoufalidis) that relates the…

Some links with non-trivial polynomials and their crossing-numbers

- Mathematics
- 1988

One of the main applications of the Jones polynomial invariant of oriented links has been in understanding links with (reduced, connected) alternating diagrams [2], [8], [9]. The Jones polynomial for…

Categorical lifting of the Jones polynomial: a survey

- Mathematics
- 2022

This is a brief review of the categorification of the Jones polynomial and its significance and ramifications in geometry, algebra, and low-dimensional topology. 1. Constructions of the Jones…

A pr 2 00 8 A state sum invariant for regular isotopy of links having a polynomial number of states by Sóstenes Lins

- Mathematics, Computer Science
- 2021

The state sum regular isotopy invariant of links, denoted VSE-invariant, is a generalization of the Jones Polynomial and is strictly stronger than Jones’: I detected a pair of links which are not distinguished byJones’ but are distinguished by the new invariant.

## References

SHOWING 1-10 OF 41 REFERENCES

A polynomial invariant for knots via von Neumann algebras

- Mathematics
- 1985

Thus, the trivial link with n components is represented by the pair (l ,n), and the unknot is represented by (si$2 * * • s n i , n) for any n, where si, $2, • • • > sn_i are the usual generators for…

Braids, link polynomials and a new algebra

- Mathematics
- 1989

A class function on the braid group is derived from the Kauffman link invariant. This function is used to construct representations of the braid groups depending on 2 parameters. The decomposition of…

Jones polynomials and classical conjectures in knot theory. II

- MathematicsMathematical Proceedings of the Cambridge Philosophical Society
- 1987

Let L be an alternating link and be its reduced (or proper) alternating diagram. Let w() denote the writhe of [3], i.e. the number of positive crossings minus the number of negative crossings. Let…

Braids : proceedings of the AMS-IMS-SIAM joint summer research conference on Artin's braid group held July 13-26, 1986 at the University of California, Santa Cruz, California

- Mathematics
- 1988

A construction of integrable differential system associated with braid groups by K. Aomoto Mapping class groups of surfaces by J. S. Birman Automorphic sets and braids and singularities by E.…

Jones’ braid-plat formula and a new surgery triple

- Mathematics
- 1988

A link Lu(2k, n 2k) is defined by a type (2k, n 2k) pairing of an n-braid Ii if the first 2 k strands are joined up as in a plat and the remaining n 2 k as in a closed braid. The main result is a…

Exactly solved models in statistical mechanics

- Physics
- 1982

exactly solved models in statistical mechanics exactly solved models in statistical mechanics rodney j baxter exactly solved models in statistical mechanics exactly solved models in statistical…

JONES: A polynomial invariant for knots via Von Neumann algebras

- Bull. Am. Math. Soc. Vol. 12, Number
- 1985

KAUFFMAN: Formal Knot Theory

- Lecture Notes No
- 1983