Algebraic & Geometric Topology

Geometry of the ${\rm SL}(3,\mathbb C)$–character variety of torus knots

Vicente Muñoz and Joan Porti

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Abstract

Let G be the fundamental group of the complement of the torus knot of type (m,n). It has a presentation G = x,yxm = yn. We find a geometric description of the character variety X(G) of characters of representations of G into SL(3, ), GL(3, ) and PGL(3, ).

Article information

Source
Algebr. Geom. Topol., Volume 16, Number 1 (2016), 397-426.

Dates
Received: 29 September 2014
Revised: 7 June 2015
Accepted: 12 June 2015
First available in Project Euclid: 16 November 2017

Permanent link to this document
https://projecteuclid.org/euclid.agt/1510841111

Digital Object Identifier
doi:10.2140/agt.2016.16.397

Mathematical Reviews number (MathSciNet)
MR3470704

Zentralblatt MATH identifier
1333.14012

Subjects
Primary: 14D20: Algebraic moduli problems, moduli of vector bundles {For analytic moduli problems, see 32G13}
Secondary: 57M25: Knots and links in $S^3$ {For higher dimensions, see 57Q45} 57M27: Invariants of knots and 3-manifolds

Keywords
torus knot characters representations

Citation

Muñoz, Vicente; Porti, Joan. Geometry of the ${\rm SL}(3,\mathbb C)$–character variety of torus knots. Algebr. Geom. Topol. 16 (2016), no. 1, 397--426. doi:10.2140/agt.2016.16.397. https://projecteuclid.org/euclid.agt/1510841111


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