## Algebraic & Geometric Topology

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

#### Abstract

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

#### Article information

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

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

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

#### 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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