## Rocky Mountain Journal of Mathematics

### The $SU(2)$-character varieties of torus knots

#### Abstract

Let $G$ be the fundamental group of the complement of the torus knot of type $(m,n)$. We study the relationship between $SU(2)$ and $\sldos$-representations of this group, looking at their characters. Using the description of the character variety of $G$, $X(G)$, we give a geometric description of $Y(G)\subset X(G)$, the set of characters arising from $SU(2)$-representations.

#### Article information

Source
Rocky Mountain J. Math., Volume 45, Number 2 (2015), 583-600.

Dates
First available in Project Euclid: 13 June 2015

https://projecteuclid.org/euclid.rmjm/1434208488

Digital Object Identifier
doi:10.1216/RMJ-2015-45-2-583

Mathematical Reviews number (MathSciNet)
MR3356629

Zentralblatt MATH identifier
1349.14048

#### Citation

Martínez-Martínez, Javier; Muñoz, Vicente. The $SU(2)$-character varieties of torus knots. Rocky Mountain J. Math. 45 (2015), no. 2, 583--600. doi:10.1216/RMJ-2015-45-2-583. https://projecteuclid.org/euclid.rmjm/1434208488