On the character variety of periodic knots and links



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Hilden, Hugh Michael and Lozano Imízcoz, María Teresa and Montesinos Amilibia, José María (2000) On the character variety of periodic knots and links. Mathematical Proceedings of the Cambridge Philosophical Society, 129 (3). pp. 477-490. ISSN 0305-0041

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Official URL: http://journals.cambridge.org/action/displayAbstract?fromPage=online&aid=64095


A link L of the 3-sphere S3 is said to be g-periodic (g≥2 an integer) if there exists an orientation preserving auto-homeomorphism h of S3 such that h(L)=L, h is of order g and the set of fixed points of h is a circle disjoint from L. A knot is called periodic with rational quotient if it is obtained as the preimage of one component of a 2-bridge link by a g-fold cyclic covering branched on the other component. In this paper the authors introduce a method to compute the excellent component of the character variety of periodic knots (note that for hyperbolic knots the excellent component of the character curve contains the complete hyperbolic structure). Among other examples, this method is applied to the seven hyperbolic periodic knots with rational quotient in Rolfsen's table and with bridge number greater than 2.

Item Type:Article
Uncontrolled Keywords:Knots and links in the 3-sphere
Subjects:Sciences > Mathematics > Topology
ID Code:22219
Deposited On:05 Jul 2013 15:31
Last Modified:12 Dec 2018 15:13

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