منابع مشابه
Peripheral Polynomials of Hyperbolic Knots
If K is a hyperbolic knot in the oriented S3, an algebraic component of its character variety containing the holonomy of the complete hyperbolic structure of finite volume of S3 \ K is an algebraic curve (excellent component K). The traces of the peripheral elements of K define polynomial functions in K. These functions are related in pairs by canonical polynomials. These peripheral polynomials...
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In [1], R.M. Kashaev introduced certain invariants of oriented links motivated by his study of quantum dilogarithm functions. Since the classical dilogarithm functions are related to the hyperbolic volumes, he naturally expected that, for hyperbolic knots, the asymptotic behaviors of his invariants determine their volumes, which is in fact confirmed for a few hyperbolic knots by himself in [2]....
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We study a twisted Alexander polynomial naturally associated to a hyperbolic knot in an integer homology 3-sphere via a lift of the holonomy representation to SL(2,C). It is an unambiguous symmetric Laurent polynomial whose coefficients lie in the trace field of the knot. It contains information about genus, fibering, and chirality, and moreover is powerful enough to sometimes detect mutation. ...
متن کاملHyperbolic Geometry of Multiply Twisted Knots
We investigate the geometry of hyperbolic knots and links whose diagrams have a high amount of twisting of multiple strands. We find information on volume and certain isotopy classes of geodesics for the complements of these links, based only on a diagram. The results are obtained by finding geometric information on generalized augmentations
متن کاملAn Algorithm to Determine the Tunnel Number of Hyperbolic Knots
The tunnel number of a knot is an important invariant. It is defined to be the minimal number of disjoint properly embedded arcs in the knot’s exterior, such that drilling out these arcs creates a handlebody. Equivalently, it is the Heegaard genus of the knot exterior minus one. However, like many other interesting knot invariants, it is hard to compute in practice. The purpose of this paper is...
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ژورنال
عنوان ژورنال: Journal of Knot Theory and Its Ramifications
سال: 2014
ISSN: 0218-2165,1793-6527
DOI: 10.1142/s0218216514500552