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ISSN (electronic): 1472-2739
ISSN (print): 1472-2747
Character varieties of double twist links

Kathleen L Petersen and Anh T Tran

Algebraic & Geometric Topology 15 (2015) 3569–3598
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.

Keywords
character variety, canonical component, double twist link
Mathematical Subject Classification 2010
Primary: 57M25
Secondary: 57N10, 14J26
References
Publication
Received: 13 November 2014
Revised: 16 April 2015
Accepted: 26 April 2015
Published: 12 January 2016
Authors
Kathleen L Petersen
Department of Mathematics
Florida State University
208 Love Building
1017 Academic Way
Tallahassee, FL 32306-4510
USA
Anh T Tran
Department of Mathematical Sciences
The University of Texas at Dallas
800 W Campbell Rd FO 35
Richardson, TX 75080
USA