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Geometry of the ${\rm SL}(3,\mathbb C)$–character variety of torus knots

Vicente Muñoz and Joan Porti

Algebraic & Geometric Topology 16 (2016) 397–426

Let G be the fundamental group of the complement of the torus knot of type (m,n). It has a presentation G = x,yxm = yn. We find a geometric description of the character variety X(G) of characters of representations of G into SL(3, ), GL(3, ) and PGL(3, ).

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torus knot, characters, representations
Mathematical Subject Classification 2010
Primary: 14D20
Secondary: 57M25, 57M27
Received: 29 September 2014
Revised: 7 June 2015
Accepted: 12 June 2015
Published: 23 February 2016
Vicente Muñoz
Facultad de Matemáticas
Universidad Complutense de Madrid
Plaza de Ciencias 3
28040 Madrid
Instituto de Ciencias Matemáticas (CSIC-UAM-UC3M-UCM)
C/ Nicolás Cabrera 15
28049 Madrid
Joan Porti
Departament de Matemàtiques
Universitat Autònoma de Barcelona
Cerdanyola del Valles
08193 Barcelona