منابع مشابه
∂-Reducing Dehn Surgeries and 1-bridge Knots
A 3-manifold is ∂-reducible if ∂M is compressible in M . By definition, this means that there is a disk D properly embedded in M so that ∂D is an essential curve in ∂M . The disk D is called a compressing disk of ∂M , or a ∂-reducing disk of M . Now suppose M is a ∂-reducible manifold. Let K be a knot in a 3-manifold M such that ∂M is incompressible in M − K. A Dehn surgery on K is called ∂-red...
متن کاملBi-twist Manifolds and Two-bridge Knots
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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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 کاملParameterizations of 1-bridge Torus Knots
A 1-bridge torus knot in a 3-manifold of genus ≤ 1 is a knot drawn on a Heegaard torus with one bridge. We give two types of normal forms to parameterize the family of 1-bridge torus knots that are similar to the Schubert’s normal form and the Conway’s normal form for 2-bridge knots. For a given Schubert’s normal form we give algorithms to determine the number of components and to compute the f...
متن کاملThe 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...
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ژورنال
عنوان ژورنال: Journal of the London Mathematical Society
سال: 2012
ISSN: 0024-6107
DOI: 10.1112/jlms/jds030