Character varieties of double twist links

Petersen, Kathleen L¹ ; Tran, Anh T²

¹Department of Mathematics, Florida State University, 208 Love Building, 1017 Academic Way, Tallahassee, FL 32306-4510, USA
²Department of Mathematical Sciences, The University of Texas at Dallas, 800 W Campbell Rd FO 35, Richardson, TX 75080, USA

Algebraic and Geometric Topology, Tome 15 (2015) no. 6, pp. 3569-3598

Résumé

We compute both natural and smooth models for the SL2(ℂ) 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 × 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(ℂ) character variety of the J(3,2m + 1) link as the surface obtained from ℙ1 × ℙ1 as a series of blow-ups.

Détail

DOI : 10.2140/agt.2015.15.3569

Classification : 57M25, 57N10, 14J26
Keywords: character variety, canonical component, double twist link

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