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The SL(2,C)-Character Varieties of Torus Knots

Muñoz, Vicente (2009) The SL(2,C)-Character Varieties of Torus Knots. Revista matemática complutense, 22 (2). pp. 489-497. ISSN 1988-2807

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Abstract

Let G be the fundamental group of the complement of the torus knot of type (m, n). This has a presentation G = < x, y vertical bar x(m) = y(n)>. We find the geometric description of the character variety X(G) of characters of representations of G into SL(2, C).


Item Type:Article
Uncontrolled Keywords:Torus knot; Characters; Representations
Subjects:Sciences > Mathematics > Algebraic geometry
Sciences > Mathematics > Topology
ID Code:17031
References:

M. Culler and P. B. Shalen, Varieties of group representations and splittings of 3-manifolds,Ann. of Math. (2) 117 (1983), no. 1, 109–146.

J. Martın-Morales and A-M. Oller-Marcen, On the varieties of representations and characters of a family of one-relator subgroups, arXiv:0805.4716.

A-M. Oller-Marc´en, The SL(2, C) character variety of a class of torus knots, Extracta Math. 23 (2008), no. 2, 163–172.

D. Rolfsen, Knots and links, Mathematics Lecture Series, vol. 7, Publish or Perish Inc., Houston,TX, 1990. Corrected reprint of the 1976 original.

Deposited On:06 Nov 2012 12:21
Last Modified:07 Feb 2014 09:40

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