Character varieties for SL(3,C): the figure eight knot

Elisha Falbel; Antonin Guilloux; Pierre-Vincent Koseleff; Fabrice Rouillier; Morwen Thistlethwaite

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arXiv · 1412.4711

Character varieties for SL(3,C): the figure eight knot

Elisha Falbel·Antonin Guilloux·Pierre-Vincent Koseleff·Fabrice Rouillier·Morwen Thistlethwaite

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Abstract

We give a description of several representation varieties of the fundamental group of the complement of the figure eight knot in PGL(3,C) or SL(3,C). We moreover obtain an explicit parametrization of matrices generating the representation and a description of the projection of the representation variety into the character variety of the boundary torus into SL(3,C).

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Elisha Falbel, Antonin Guilloux, Pierre-Vincent Koseleff, Fabrice Rouillier, Morwen Thistlethwaite. 2014-12-15. Character varieties for SL(3,C): the figure eight knot. https://arxiv.org/abs/1412.4711

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