The SU(2)-character varieties of torus knots

2012/02/15 by J. Martı́nez-Martı́nez, Vicente Muñoz, Martínez-Martínez, Javier +1
Mathematics · #Geometric and Algebraic Topology #Homotopy and Cohomology in Algebraic Topology #Algebraic structures and combinatorial models

paper · pdf · doi:10.48550/arxiv.1202.3241

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 SL(2,C)-representations of this group, looking at their characters. Using the description of the SL(2,C)-character variety of G, X(G), we give a geometric description of Y(G)⊂ X(G), the set of characters arising from SU(2)-representations.

Related

• The SL(2,C)-character varieties of torus knots
• Geometry of SU(3)-character varieties of torus knots
• Character varieties of torus links
• Character varieties for SL(3,C): the figure eight knot
• Torus-covering knot groups and their irreducible metabelian SU(2)-representations