A class of two-bridge knots with property-$P$
نویسندگان
چکیده
منابع مشابه
A-polynomials of a Family of Two-bridge Knots
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...
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We show that every two-bridge knot K of crossing number N admits a polynomial parametrization x = T3(t), y = Tb(t), z = C(t) where Tk(t) are the Chebyshev polynomials and b + degC = 3N . If C(t) = Tc(t) is a Chebyshev polynomial, we call such a knot a harmonic knot. We give the classification of harmonic knots for a ≤ 3. Most results are derived from continued fractions and their matrix represe...
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We give uniform, explicit, and simple face-pairing descriptions of all the branched cyclic covers of the 3–sphere, branched over two-bridge knots. Our method is to use the bi-twisted face-pairing constructions of Cannon, Floyd, and Parry; these examples show that the bi-twist construction is often efficient and natural. Finally, we give applications to computations of fundamental groups and hom...
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We prove that knots with braid index three in the 3-sphere satisfy the Property P conjecture.
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In this paper, we show that, for each non-trivial two bridge knot K and for each g ≥ 3, every genus g Heegaard splitting of the exterior E(K) of K is reducible. AMS Classification numbers Primary: 57M25 Secondary: 57M05
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ژورنال
عنوان ژورنال: Proceedings of the American Mathematical Society
سال: 1977
ISSN: 0002-9939
DOI: 10.1090/s0002-9939-1977-0448335-8