The colored Jones polynomial and the A-polynomial of Knots
نویسندگان
چکیده
منابع مشابه
The Colored Jones Polynomial and the A-polynomial of Knots
We study relationships between the colored Jones polynomial and the A-polynomial of a knot. The AJ conjecture (of Garoufalidis) that relates the colored Jones polynomial and the A-polynomial is established for a large class of two-bridge knots, including all twist knots. We formulate a weaker conjecture and prove that it holds for all two-bridge knots. Along the way we also calculate the Kauffm...
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We generalize the colored Jones polynomial to 4-valent graphs. This generalization is given as a sequence of invariants in which the first term is a one variable specialization of the Kauffman–Vogel polynomial. We use the invariant we construct to give a sequence of singular braid group representations.
متن کاملThe Colored Jones Polynomial and the A-polynomial of Two-bridge Knots
We study relationships between the colored Jones polynomial and the A-polynomial of a knot. We establish for a large class of 2-bridge knots the AJ conjecture (of Garoufalidis) that relates the colored Jones polynomial and the A-polynomial. Along the way we also calculate the Kauffman bracket skein module of all 2-bridge knots. Some properties of the colored Jones polynomial of alternating knot...
متن کاملThe Colored Jones Polynomial and the A-polynomial for Twist Knots
@We show that for a twist knot, the A-polynomial can be obtained from recurrences for the summand in Masbaum’s formula of the colored Jones polynomial. Our result supports the AJ conjecture due to S.Garoufalidis.
متن کاملAsymptotics of the Colored Jones Polynomial and the A-polynomial
The N-colored Jones polynomial JK (N) is a quantum invariant which is defined based on the N-dimensional irreducible representation of the quantum group Uq(sl(2)). Motivated by Volume Conjecture raised by Kashaev [16], it was pointed out that the colored Jones polynomial at a specific value should be related to the hyperbolic volume of knot complement [21]. As another example of the knot invari...
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ژورنال
عنوان ژورنال: Advances in Mathematics
سال: 2006
ISSN: 0001-8708
DOI: 10.1016/j.aim.2006.01.006