#### Volume 16, issue 1 (2016)

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

### Vicente Muñoz and Joan Porti

Algebraic & Geometric Topology 16 (2016) 397–426
##### Abstract

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

##### Keywords
torus knot, characters, representations
##### Mathematical Subject Classification 2010
Primary: 14D20
Secondary: 57M25, 57M27