A matrix for computing the Jones polynomial of a knot
نویسندگان
چکیده
منابع مشابه
Is the Jones Polynomial of a Knot Really a Polynomial?
The Jones polynomial of a knot in 3-space is a Laurent polynomial in q, with integer coefficients. Many people have pondered why is this so, and what is a proper generalization of the Jones polynomial for knots in other closed 3-manifolds. Our paper centers around this question. After reviewing several existing definitions of the Jones polynomial, we show that the Jones polynomial is really an ...
متن کاملDoes the Jones Polynomial Determine the Signature of a Knot?
The signature function of a knot is an integer valued step function defined on the unit circle. The jumps (i.e., the discontinuities) of the signature function can occur only at the roots of the Alexander polynomial on the unit circle. The latter are important in deforming U(1) representations of knot groups to irreducible SU(2) representations. Under the assumption that these roots are simple,...
متن کاملThe Knot Group and The Jones Polynomial
In this thesis, basic knot theory is introduced, along with concepts from topology, algebra and algebraic topology, as they relate to knot theory. In the first chapter, basic definitions concerning knots are presented. In the second chapter, the fundamental group is applied as a method of distinguishing knots. In particular the torus knots are classified using the fundamental group, and a gener...
متن کاملThe Jones Polynomial, Genus and Weak Genus of a Knot
In his book [Ad, p. 105 bottom], C. Adams mentions a result of Morton that there exist knots, whose genus g is strictly less than their weak genus g̃, the minimal genus of (the surface of Seifert’s algorithm applied on) all their diagrams. This observation appears just as a remark in [Mo], but was very striking to the author. Motivated by Morton’s example, the author started in a series of paper...
متن کاملDifference Equation of the Colored Jones Polynomial for Torus Knot
The N-colored Jones polynomial JK (N) is one of the quantum invariants for knot K . It is associated with the N-dimensional irreducible representation of sl(2), and is powerful to classify knots. Motivated by “volume conjecture” [12, 18] saying that a hyperbolic volume of the knot complement dominates an asymptotic behavior of the colored Jones polynomial JK (N) at q = e2πi/N , it receives much...
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ژورنال
عنوان ژورنال: Topology
سال: 1995
ISSN: 0040-9383
DOI: 10.1016/0040-9383(94)00041-i