• Corpus ID: 237365114

On the Jones Polynomial

@inproceedings{Queen2021OnTJ,
  title={On the Jones Polynomial},
  author={M. Abila Jeba Queen},
  year={2021}
}
  • M. Queen
  • Published 27 August 2021
  • Mathematics
This expository essay is aimed at introducing the Jones polynomial. We will see the encapsulation of the Jones polynomial, which will involve topics in functional analysis and geometrical topology; making this essay an interdisciplinary area of mathematics. The presentation is based on a lot of different sources of material (check references), but we will mainly be giving an account on Jones’ papers ([25],[26],[27],[28],[29]) and Kauffman’s papers ([33],[34],[35]). A background in in… 

References

SHOWING 1-10 OF 50 REFERENCES
Invariants of links of Conway type
The purpose of this paper is to present a certain combinatorial method of constructing invariants of isotopy classes of oriented tame links. This arises as a generalization of the known polynomial
On the computational complexity of the Jones and Tutte polynomials
Abstract We show that determining the Jones polynomial of an alternating link is #P-hard. This is a special case of a wide range of results on the general intractability of the evaluation of the
A Polynomial Quantum Algorithm for Approximating the Jones Polynomial
TLDR
An explicit and simplePolynomial quantum algorithm to approximate the Jones polynomial of an n strands braid with m crossings at any primitive root of unity e2πi/k, where the running time of the algorithm is polynometric in m, n and k.
A polynomial invariant for knots via von Neumann algebras
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
Representation of links by braids: A new algorithm
If a is a braid with n components, the closure of a, denoted #, is constructed by connecting the endpoints at the top level to the bottom endpoints with n standard curves. This procedure yields an
A new polynomial invariant of knots and links
The purpose of this note is to announce a new isotopy invariant of oriented links of tamely embedded circles in 3-space. We represent links by plane projections, using the customary conventions that
Hecke algebra representations of braid groups and link polynomials
By studying representations of the braid group satisfying a certain quadratic relation we obtain a polynomial invariant in two variables for oriented links. It is expressed using a trace, discovered
On the Group of All Homeomorphisms of a Manifold.
Introduction. It is shown in this paper that the identity component of the group G(M) of all homeomorphisms-of a closed manifold of dimension <3 is (1) simple in the algebraic sense; (2) equal to the
A Lemma on Systems of Knotted Curves.
  • J. W. Alexander
  • Mathematics
    Proceedings of the National Academy of Sciences of the United States of America
  • 1923
continuous correspondences on a Riemann surface, whether algebraic or not, uithout recourse to transcendental considerations. (d) Open manifolds. Here an adaptation of a reasoning due to Alexander
...
...