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Peripheral polynomials of hyperbolic knots

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Hilden, Hugh Michael and Lozano Imízcoz, María Teresa and Montesinos Amilibia, José María (2005) Peripheral polynomials of hyperbolic knots. Topology and its Applications, 150 (1-3). pp. 267-288. ISSN 0166-8641

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Official URL: http://www.sciencedirect.com/science/article/pii/S0166864104003840




Abstract

If K is a hyperbolic knot in S3, an algebraic component of its character variety containing one holonomy of the complete hyperbolic structure of finite volume of S3∖K is an algebraic curve K. The traces of the peripheral elements of K define polynomial functions in K, which are related in pairs by polynomials (peripheral polynomials). These are determined by just two adjacent peripheral polynomials. The curves defined by the peripheral polynomials are all birationally equivalent to K, with only one possible exception. The canonical peripheral polynomial relating the trace of the meridian with the trace of the canonical longitude of K is a factor of the A-polynomial.


Item Type:Article
Uncontrolled Keywords:Character variety; Hyperbolic knot
Subjects:Sciences > Mathematics > Algebraic geometry
Sciences > Mathematics > Topology
ID Code:22345
Deposited On:12 Jul 2013 12:52
Last Modified:12 Dec 2018 15:13

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