منابع مشابه
Covering Spaces over Claspered Knots
In this note we reconsider a familiar result in Vassiliev knot theory that the coefficients of the Alexander-Conway polynomial determine the top row of the Kontsevich integral from the point of view of Kazuo Habiro’s clasper theory. We observe that in this setting the calculation reflects the topology of the universal cyclic covering space of a claspered knot’s complement.
متن کاملPeripheral 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...
متن کاملTwisted Alexander Polynomials of Hyperbolic Knots
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
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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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ژورنال
عنوان ژورنال: Algebraic & Geometric Topology
سال: 2005
ISSN: 1472-2739,1472-2747
DOI: 10.2140/agt.2005.5.1451