The SL(2,C)-character varieties of torus knots

2009/01/13 by Vicente Muñoz, Muñoz, Vicente
Mathematics · #14D200 #57M25 #57M27 #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Geometric and Algebraic Topology #Homotopy and Cohomology in Algebraic Topology

paper · pdf · doi:10.48550/arxiv.0901.1783

openalex publication_date 2009/01/13 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/02

Abstract

Let G be the fundamental group of the complement of the torus knot of type (m,n). This has a presentation G=. We find the geometric description of the character variety X(G) of characters of representations of G into SL(2,C).

Related

• The SU(2)-character varieties of torus knots
• Character varieties for SL(3,C): the figure eight knot
• Character varieties of torus links
• Geometry of SU(3)-character varieties of torus knots
• The SL(3,C)-character variety of the figure eight knot