The Colored Jones Polynomial and the A-polynomial for Twist Knots
نویسنده
چکیده
@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.
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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The AJ conjecture relates the A-polynomial and the colored Jones polynomial of a knot in the 3-sphere. It has been verified for some classes of knots, including all torus knots, most double twist knots, (−2, 3, 6n ± 1)-pretzel knots, and most cabled knots over torus knots. In this paper we study the AJ conjecture for (r, 2)-cables of a knot, where r is an odd integer. In particular, we show tha...
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...
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تاریخ انتشار 2004