The SU(2)-character varieties of torus knots

Javier Martínez-Martínez, Vicente Muñoz

Published 2012-02-15, updated 2012-02-23Version 2

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)\subset X(G), the set of characters arising from SU(2)-representations.