Geodesic
Geometry of the SL(3, ℂ)–character variety of torus knots
Muñoz, Vicente1 ; Porti, Joan2
1Facultad de Matemáticas, Universidad Complutense de Madrid, Plaza de Ciencias 3, 28040 Madrid, Spain, Instituto de Ciencias Matemáticas (CSIC-UAM-UC3M-UCM), C/ Nicolás Cabrera 15, 28049 Madrid, Spain
2Departament de Matemàtiques, Universitat Autònoma de Barcelona, Cerdanyola del Valles, 08193 Barcelona, Spain
Algebraic and Geometric Topology, Tome 16 (2016) no. 1, pp. 397-426
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Let G be the fundamental group of the complement of the torus knot of type (m,n). It has a presentation G = 〈x,y∣xm = yn〉. We find a geometric description of the character variety X(G) of characters of representations of G into SL(3, ℂ), GL(3, ℂ) and PGL(3, ℂ).

DOI : 10.2140/agt.2016.16.397
Classification : 14D20, 57M25, 57M27
Keywords: torus knot, characters, representations

Muñoz, Vicente  1   ; Porti, Joan  2

1 Facultad de Matemáticas, Universidad Complutense de Madrid, Plaza de Ciencias 3, 28040 Madrid, Spain, Instituto de Ciencias Matemáticas (CSIC-UAM-UC3M-UCM), C/ Nicolás Cabrera 15, 28049 Madrid, Spain
2 Departament de Matemàtiques, Universitat Autònoma de Barcelona, Cerdanyola del Valles, 08193 Barcelona, Spain 
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Muñoz, Vicente; Porti, Joan. Geometry of the SL(3, ℂ)–character variety of torus knots. Algebraic and Geometric Topology, Tome 16 (2016) no. 1, pp. 397-426. doi: 10.2140/agt.2016.16.397

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