Symmetric links and {C}onway sums: volume and {J}ones polynomial
نویسندگان
چکیده
منابع مشابه
Symmetric 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.
متن کاملDehn Filling, Volume, and the Jones Polynomial
Given a hyperbolic 3–manifold with torus boundary, we bound the change in volume under a Dehn filling where all slopes have length at least 2π. This result is applied to give explicit diagrammatic bounds on the volumes of many knots and links, as well as their Dehn fillings and branched covers. Finally, we use this result to bound the volumes of knots in terms of the coefficients of their Jones...
متن کاملThe 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 کاملA Refined Jones Polynomial for Symmetric Unions
Motivated by the study of ribbon knots we explore symmetric unions, a beautiful construction introduced by Kinoshita and Terasaka in 1957. We develop a twovariable refinement WD(s,t) of the Jones polynomial that is invariant under symmetric Reidemeister moves. If D is a symmetric union diagram, representing a ribbon knot K, then the polynomial WD(s,t) nicely reflects their topological propertie...
متن کاملChirality and the Conway Polynomial
We conjecture that for the Conway polynomial C(z) of an amphicheiral knot, the product C(z)C(iz)C(z 2) must be a square inside the ring of polynomials with Z 4 coefficients. This conjecture has two ancestors. One is a theorem of Kawauchi and Hartley, which says that the Conway polynomial of a strongly amphicheiral knot must decompose as φ(z)φ(−z). This implies our main conjecture, at least for ...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Mathematical Research Letters
سال: 2009
ISSN: 1073-2780,1945-001X
DOI: 10.4310/mrl.2009.v16.n2.a3