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On the character variety of group representations of a 2-bridge link p/3 into PSL(2,C)

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Hilden, Hugh Michael and Lozano Imízcoz, María Teresa and Montesinos Amilibia, José María (1992) On the character variety of group representations of a 2-bridge link p/3 into PSL(2,C). Boletín de la Sociedad Matemática Mexicana. Segunda Serie, 37 (1-2). pp. 241-262. ISSN 0037-8615



Abstract

Consider the group G of a classical knot or link in S3. It is natural to consider the representations of G into PSL(2,C). The set of conjugacy classes of nonabelian representations is a closed algebraic set called the character variety (of representations of G into PSL(2,C)). If G is the group of a 2-bridge knot or link, then a polynomial results by an earlier published theorem of the authors. This polynomial is related to the Morgan-Voyce polynomials Bn(z), which can be defined by the formulas pn(z)=Bn(z−2), where pn=zpn−1−pn−2, p0=1, p1=z, or
(z1−10)n=(pnpn−1−pn−1−pn−2).
In this paper the authors do many calculations for classes of 2-bridge knots or links.


Item Type:Article
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Papers in honor of José Adem (Spanish)

Uncontrolled Keywords:conjugacy classes of non-abelian representations; fundamental groups; compact 3-manifolds; generators; relators; 2-bridge knots; closed formula; character variety; arithmeticity of orbifolds
Subjects:Sciences > Mathematics > Differential geometry
Sciences > Mathematics > Topology
ID Code:22144
Deposited On:27 Jun 2013 16:54
Last Modified:12 Dec 2018 15:13

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