Rocky Mountain Journal of Mathematics

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

Javier Martínez-Martínez and Vicente Muñoz

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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

Permanent link to this document
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

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

Keywords
Torus knot character variety representations

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


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