Algebraic & Geometric Topology

Character varieties of double twist links

Kathleen L Petersen and Anh T Tran

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Abstract

We compute both natural and smooth models for the SL2() character varieties of the two-component double twist links, an infinite family of two-bridge links indexed as J(k,l). For each J(k,l), the component(s) of the character variety containing characters of irreducible representations are birational to a surface of the form C × , where C is a curve. The same is true of the canonical component. We compute the genus of this curve, and the degree of irrationality of the canonical component. We realize the natural model of the canonical component of the SL2() character variety of the J(3,2m + 1) link as the surface obtained from 1 × 1 as a series of blow-ups.

Article information

Source
Algebr. Geom. Topol., Volume 15, Number 6 (2015), 3569-3598.

Dates
Received: 13 November 2014
Revised: 16 April 2015
Accepted: 26 April 2015
First available in Project Euclid: 16 November 2017

Permanent link to this document
https://projecteuclid.org/euclid.agt/1510841077

Digital Object Identifier
doi:10.2140/agt.2015.15.3569

Mathematical Reviews number (MathSciNet)
MR3450771

Zentralblatt MATH identifier
1360.57021

Subjects
Primary: 57M25: Knots and links in $S^3$ {For higher dimensions, see 57Q45}
Secondary: 57N10: Topology of general 3-manifolds [See also 57Mxx] 14J26: Rational and ruled surfaces

Keywords
character variety canonical component double twist link

Citation

Petersen, Kathleen L; Tran, Anh T. Character varieties of double twist links. Algebr. Geom. Topol. 15 (2015), no. 6, 3569--3598. doi:10.2140/agt.2015.15.3569. https://projecteuclid.org/euclid.agt/1510841077


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