Geometry of the SL(3, ℂ)–character variety of torus knots

Muñoz, Vicente; Porti, Joan

doi:10.2140/agt.2016.16.397

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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

DOI: 10.2140/agt.2016.16.397

Abstract

Let $G$ be the fundamental group of the complement of the torus knot of type $(m, n)$ . It has a presentation $G = 〈 x, y ∣ x^{m} = y^{n} 〉$ . We find a geometric description of the character variety $X (G)$ of characters of representations of $G$ into $S L (3, ℂ)$ , $G L (3, ℂ)$ and $P G L (3, ℂ)$ .

Keywords

torus knot, characters, representations

Mathematical Subject Classification 2010

Primary: 14D20

Secondary: 57M25, 57M27

References

Publication

Received: 29 September 2014

Revised: 7 June 2015

Accepted: 12 June 2015

Published: 23 February 2016

Authors

Vicente Muñoz
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
http://www.mat.ucm.es/~vmunozve/
Joan Porti
Departament de Matemàtiques Universitat Autònoma de Barcelona Cerdanyola del Valles 08193 Barcelona Spain
http://mat.uab.es/~porti/

Volume 16, issue 1 (2016)