منابع مشابه
The Jones polynomial of ribbon links
For every n–component ribbon link L we prove that the Jones polynomial V(L) is divisible by the polynomial V(©n) of the trivial link. This integrality property allows us to define a generalized determinant det V(L) := [V(L)/V(©)](t 7→−1) , for which we derive congruences reminiscent of the Arf invariant: every ribbon link L = K1∪· · ·∪Kn satisfies det V(L) ≡ det(K1) · · · det(Kn) modulo 32, whe...
متن کاملOn the colored Jones polynomials of ribbon links, boundary links and Brunnian links
Habiro gave principal ideals of Z[q, q−1] in which certain linear combinations of the colored Jones polynomials of algebraically-split links take values. The author proved that the same linear combinations for ribbon links, boundary links and Brunnian links are contained in smaller ideals of Z[q, q−1] generated by several elements. In this paper, we prove that these ideals also are principal, e...
متن کاملIntegrality of the Averaged Jones Polynomial of Algebraically Split Links
n!φn(L) ∈ 6Z. This conjecture is verified for n = 1, 2 in [LW], and we consider the case n ≥ 3 here. We first establish that an(L) ∈ Z whenever L is a geometrically split link (GSL), implying that φn(L) ∈ 2Z, which is a priori stronger than the conjecture in this case. Nevertheless, Conjecture 4.1 is not true for ASLs. The problem is the presence of additional factors of 2 in the denominator of...
متن کاملInfinite families of links with trivial Jones polynomial
For each k ≥ 2, we exhibit infinite families of prime k-component links with Jones polynomial equal to that of the k-component unlink.
متن کاملSymmetric Links and Conway Sums: Volume and Jones Polynomial
We obtain bounds on hyperbolic volume for periodic links and Conway sums of alternating tangles. For links that are Conway sums we also bound the hyperbolic volume in terms of the coefficients of the Jones polynomial.
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ژورنال
عنوان ژورنال: Geometry & Topology
سال: 2009
ISSN: 1364-0380,1465-3060
DOI: 10.2140/gt.2009.13.623