Colored Jones Invariants of Links In
نویسنده
چکیده
We extend the definition of the colored Jones polynomials to framed links and trivalent graphs in S3#kS 2 × S using a state-sum formulation based on Turaev’s shadows. Then, we prove that the natural extension of the Volume Conjecture is true for an infinite family of hyperbolic links.
منابع مشابه
COLORED JONES INVARIANTS OF LINKS IN S 3 #kS 2 × S 1 AND THE VOLUME CONJECTURE
We extend the definition of the colored Jones polynomials to framed links and trivalent graphs in S3#kS 2 × S using a state-sum formulation based on Turaev’s shadows. Then, we prove that the natural extension of the Volume Conjecture is true for an infinite family of hyperbolic links.
متن کاملThe Colored Jones Polynomials and the Simplicial Volume of a Knot
We show that the set of colored Jones polynomials and the set of generalized Alexander polynomials defined by Akutsu, Deguchi and Ohtsuki intersect non-trivially. Moreover it is shown that the intersection is (at least includes) the set of Kashaev’s quantum dilogarithm invariants for links. Therefore Kashaev’s conjecture can be restated as follows: The colored Jones polynomials determine the hy...
متن کاملKashaev's Conjecture and the Chern-Simons Invariants of Knots and Links
Abstract. R.M. Kashaev conjectured that the asymptotic behavior of his link invariant, which equals the colored Jones polynomial evaluated at a root of unity, determines the hyperbolic volume of any hyperbolic link complement. We observe numerically that for knots 63, 89 and 820 and for the Whitehead link, the colored Jones polynomials are related to the hyperbolic volumes and the Chern–Simons ...
متن کاملInvariants of Colored Links and a Property of the Clebsch-gordan Coefficients of U Q (g)
Abstract. We show that multivariable colored link invariants are derived from the roots of unity representations of Uq(g). We propose a property of the Clebsch-Gordan coefficients of Uq(g), which is important for defining the invariants of colored links. For Uq(sl2) we explicitly prove the property, and then construct invariants of colored links and colored ribbon graphs, which generalize the m...
متن کاملColored Tutte Polynomials and Kauuman Brackets for Graphs of Bounded Tree Width
Jones polynomials and Kauuman polynomials are the most prominent invariants of knot theory. For alternating links, they are easily computable from the Tutte polynomials by a result of Thistlethwaite (1988), but in general one needs colored Tutte polynomials, as introduced by Bollobas and Riordan (1999). Knots and links can be presented as labeled planar graphs. The tree width of a link L is dee...
متن کامل