scholarly journals Using Quandles and the Alexander-Conway Polynomial to Detect Causality

2021 ◽  
Author(s):  
Joshua Piesner
Keyword(s):  
Conway Polynomial

scholarly journals Computing the Conway polynomial of several closures of oriented 3-braids

2012 ◽  
Vol 159 (4) ◽  
pp. 1195-1209
Author(s):  
David A. Lizárraga-Navarro ◽  
Hugo Cabrera-Ibarra ◽  
Leila Y. Hernández-Villegas
Keyword(s):  
Conway Polynomial

Conway Polynomial and Oriented Rotant Links

2005 ◽  
Vol 110 (1) ◽  
pp. 49-61
Author(s):  
Pawel Traczyk
Keyword(s):  
Conway Polynomial

On Weight Systems Derived from Heisenberg Lie Algebras

2003 ◽  
Vol 12 (05) ◽  
pp. 589-604
Author(s):  
Hideaki Nishihara
Keyword(s):  
Lie Algebra ◽  
Lie Algebras ◽  
Weight System ◽  
Infinite Dimensional ◽  
Conway Polynomial ◽  
Knot Invariant ◽  
Polynomial Representations ◽  
Solvable Lie Algebras

Weight systems are constructed with solvable Lie algebras and their infinite dimensional representations. With a Heisenberg Lie algebra and its polynomial representations, the derived weight system vanishes on Jacobi diagrams with positive loop-degree on a circle, and it is proved that the derived knot invariant is the inverse of the Alexander-Conway polynomial.

scholarly journals On a Realization of Prime Tangles and Knots

1983 ◽  
Vol 35 (2) ◽  
pp. 311-323
Author(s):  
Quach Thi Cam Van
Keyword(s):  
Alexander Polynomial ◽  
Conway Polynomial ◽  
Natural Means ◽  
Natural Way

The notion of a prime tangle is introduced by Kirby and Lickorish [7]. It is related deeply to the notion of a prime knot by the following result in [8]: summing together two prime tangles gives always a prime knot.The purpose of this paper is to exploit this above mentioned result of Lickorish in creating or detecting prime knots which satisfy certain properties. First, we shall express certain knots (two-bridge knots and Terasaka slice knots [14]) as a sum of a prime tangle and an untangle (the existence of such a sum is proven to every knot in [7] and is not unique) in a natural way (natural means here depending on certain specific geometrical characters of the class of knots). Second, every Alexander polynomial (or Conway polynomial) is shown to be realized by a prime algebraic knot (algebraic in the sense of Conway [3], Bonahon-Siebenmann [2]) which can be expressed as the sum of two prime algebraic tangles.

III. THE CONWAY POLYNOMIAL

1988 ◽  
pp. 19-41
Keyword(s):  
Conway Polynomial

scholarly journals An Orientation-Sensitive Vassiliev Invariant for Virtual Knots

2003 ◽  
Vol 12 (06) ◽  
pp. 767-779 ◽  
Author(s):  
Jörg Sawollek
Keyword(s):  
Virtual Link ◽  
Zeroth Order ◽  
Opposite Orientation ◽  
Vassiliev Invariants ◽  
Virtual Knot ◽  
First Order ◽  
Virtual Knots ◽  
Conway Polynomial ◽  
Vassiliev Invariant ◽  
Open Question

It is an open question whether there are Vassiliev invariants that can distinguish an oriented knot from its inverse, i.e., the knot with the opposite orientation. In this article, an example is given for a first order Vassiliev invariant that takes different values on a virtual knot and its inverse. The Vassiliev invariant is derived from the Conway polynomial for virtual knots. Furthermore, it is shown that the zeroth order Vassiliev invariant coming from the Conway polynomial cannot distinguish a virtual link from its inverse and that it vanishes for virtual knots.

LOCAL MOVES AND GORDIAN COMPLEXES

2006 ◽  
Vol 15 (09) ◽  
pp. 1215-1224 ◽  
Author(s):  
YASUTAKA NAKANISHI ◽  
YOSHIYUKI OHYAMA
Keyword(s):  
Vassiliev Invariants ◽  
Conway Polynomial ◽  
Vassiliev Invariant ◽  
The Relationship

By the works of Gusarov [2] and Habiro [3], it is known that a local move called the Cnmove is strongly related to Vassiliev invariants of order less than n. The coefficient of the znterm in the Conway polynomial is known to be a Vassiliev invariant of order n. In this note, we will consider to what degree the relationship is strong with respect to Conway polynomial. Let K be a knot, and KCnthe set of knots obtained from a knot K by a single Cnmove. Let [Formula: see text] be the set of the Conway polynomials [Formula: see text] for a set of knots [Formula: see text]. Our main result is the following: There exists a pair of knots K1, K2such that ∇K1= ∇K2and [Formula: see text]. In other words, the CnGordian complex is not homogeneous with respect to Conway polynomial.

Quantum field theory for the multi-variable Alexander-Conway polynomial

1992 ◽  
Vol 376 (3) ◽  
pp. 461-509 ◽  
Author(s):  
L. Rozansky ◽  
H. Saleur
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Quantum Field ◽  
Conway Polynomial

FIRST COMMON TERMS OF THE HOMFLY AND KAUFFMAN POLYNOMIALS, AND THE CONWAY POLYNOMIAL OF A KNOT

1999 ◽  
Vol 08 (04) ◽  
pp. 447-462 ◽  
Author(s):  
HIROZUMI FUJII
Keyword(s):  
Polynomial Invariants ◽  
Conway Polynomial ◽  
Vassiliev Invariant ◽  
Order Four

We study the first common terms of the HOMFLY and Kauffman polynomials of a knot, which we call the ϒ-polynomial, and the Conway polynomial for the 2-bridge knots and a class of 3-bridge knots. We characterize the ϒ-polynomial using the 2-bridge knots. Then we give some relations between the two polynomial invariants, and as an application, we consider the space of the Vassiliev invariant of order four.

scholarly journals PLANE REAL ALGEBRAIC CURVES OF ODD DEGREE WITH A DEEP NEST

2005 ◽  
Vol 14 (04) ◽  
pp. 497-522 ◽  
Author(s):  
STEPAN YU. OREVKOV
Keyword(s):  
Algebraic Curves ◽  
Base Case ◽  
Induction Step ◽  
Real Algebraic Curves ◽  
Conway Polynomial ◽  
Odd Degree ◽  
Skein Relation ◽  
Torus Links

We apply the Murasugi–Tristram inequality to real algebraic curves of odd degree in RP2 with a deep nest, i.e. a nest of the depth k - 1 where 2k + 1 is the degree. For such curves, the ingredients of the Murasugi–Tristram inequality can be computed (or estimated) inductively using the computations for iterated torus links due to Eisenbud and Neumann as the base case of the induction and Conway's skein relation as the induction step. As an example of applications, we prove that some isotopy types are not realizable by M-curves of degree 9. In Appendix B, we give some generalization of the skein relation for Conway polynomial.

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