A note on Riley polynomials of 2-bridge knots
نویسندگان
چکیده
منابع مشابه
The Kauffman Polynomials of 2-bridge Knots
The 2-bridge knots (or links) are a family of knots with bridge number 2. A 2bridge knot (link) has at most 2 components. Except for the knot 85, the first 25 knots in the Rolfsen Knot Table are 2-bridge knots. A 2-bridge knot is also called a rational knot because it can be obtained as the numerator or denominator closure of a rational tangle. The rich mathematical aspects of 2-bridge knots ca...
متن کاملUpper bounds in the Ohtsuki-Riley-Sakuma partial order on 2-bridge knots
In this paper we use continued fractions to study a partial order on the set of 2-bridge knots derived from the work of Ohtsuki, Riley, and Sakuma. We establish necessary and sufficient conditions for any set of 2-bridge knots to have an upper bound with respect to the partial order. Moreover, given any 2-bridge knot K1 we characterize all other 2-bridge knots K2 such that {K1,K2} has an upper ...
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The J(k, l) knots, often called the double twist knots, are a subclass of two-bridge knots which contains the twist knots. We show that the A-polynomial of these knots can be determined by an explicit resultant. We present this resultant in two different ways. We determine a recursive definition for the A-polynomials of the J(4, 2n) and J(5, 2n) knots, and for the canonical component of the A-p...
متن کاملUniqueness of bridge surfaces for 2-bridge knots
Any 2-bridge knot in S has a bridge sphere from which any other bridge surface can be obtained by stabilization, meridional stabilization, perturbation and proper isotopy.
متن کاملThe Classification of Dehn Surgeries on 2-bridge Knots
We will determine whether a given surgery on a 2-bridge knot is reducible, toroidal, Seifert bered, or hyperbolic. In [Th1] Thurston showed that if K is a hyperbolic knot, then all but nitely many surgeries on K are hyperbolic. In particular, for the Figure 8 knot, it was shown that exactly 9 nontrivial surgeries are non-hyperbolic. Let Kp=q be a 2-bridge knot associated to the rational number ...
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ژورنال
عنوان ژورنال: Annales de la faculté des sciences de Toulouse Mathématiques
سال: 2017
ISSN: 0240-2963,2258-7519
DOI: 10.5802/afst.1565