منابع مشابه
Characterizing slopes for torus knots
A slope p q is called a characterizing slope for a given knot K0 in S if whenever the p q –surgery on a knot K in S is homeomorphic to the p q –surgery on K0 via an orientation preserving homeomorphism, then K D K0 . In this paper we try to find characterizing slopes for torus knots Tr;s . We show that any slope p q which is larger than the number 30.r 1/.s 1/=67 is a characterizing slope for T...
متن کاملSlopes for pretzel knots
Using the Hatcher–Oertel algorithm for finding boundary slopes of Montesinos knots, we prove the Slope Conjecture and the Strong Slope Conjecture for a family of 3-tangle pretzel knots. More precisely, we prove that the maximal degrees of the colored Jones polynomial of such a knot determine a boundary slope as predicted by the Slope Conjecture, and that the linear terms in the degrees correspo...
متن کاملBoundary Slopes for Montesinos Knots
FOR A KNOT K c S3, let S(K) c Q u {CQ} be the set of slopes of boundary curves of incompressible, %incompressible orientable surfaces in the knot exterior, slopes being normalized in the standard way so that a longitude has slope 0, a meridian slope co. These sets S(K) of %slopes are of special interest because of their relation with Dehn surgery and character varieties; see e.g., [2]. The only...
متن کاملVassiliev Invariants for Torus Knots
Vassiliev invariants up to order six for arbitrary torus knots {n,m}, with n and m coprime integers, are computed. These invariants are polynomials in n and m whose degree coincide with their order. Furthermore, they turn out to be integer-valued in a normalization previously proposed by the authors. ⋆ e-mail: [email protected]
متن کاملUnknotting Sequences for Torus Knots
The unknotting number of a knot is bounded from below by its slice genus. It is a well-known fact that the genera and unknotting numbers of torus knots coincide. In this note we characterize quasipositive knots for which the genus bound is sharp: the slice genus of a quasipositive knot equals its unknotting number, if and only if the given knot appears in an unknotting sequence of a torus knot.
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ژورنال
عنوان ژورنال: Algebraic & Geometric Topology
سال: 2014
ISSN: 1472-2739,1472-2747
DOI: 10.2140/agt.2014.14.1249