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On SL(3,\({\varvec{\mathbb {C}}}\))-representations of the Whitehead link group

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Abstract

We describe a family of representations in SL(3,\(\mathbb {C}\)) of the fundamental group \(\pi \) of the Whitehead link complement. These representations are obtained by considering pairs of regular order three elements in SL(3,\(\mathbb {C}\)) and can be seen as factoring through a quotient of \(\pi \) defined by a certain exceptional Dehn surgery on the Whitehead link. Our main result is that these representations form an algebraic component of the SL(3,\(\mathbb {C}\))-character variety of \(\pi \).

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Notes

  1. We drop here the indication of the tetrahedron \(\Delta _\nu \) for \(0\leqslant \nu \leqslant 3\) in order to simplify the notations.

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Acknowledgements

We wish to thank Miguel Acosta, Martin Deraux, Elisha Falbel, Michael Heusener and John Parker for numerous stimulating conversations. We thank Neil Hofmann, Craig Hodgson, Bruno Martelli and Carlo Petronio for kindly answering our questions. We also thank the anonymous referee for his/her help to improve our work.

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Authors and Affiliations

  1. IMJ-PRG, Sorbonne Université and OURAGAN, INRIA, 4 place Jussieu, 75005, Paris, France

    Antonin Guilloux

  2. Institut Fourier, Université Grenoble Alpes, B.P. 74, 38402, Saint-Martin-d’Hères Cedex, France

    Pierre Will

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  1. Antonin Guilloux
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Correspondence to Pierre Will.

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Guilloux, A., Will, P. On SL(3,\({\varvec{\mathbb {C}}}\))-representations of the Whitehead link group. Geom Dedicata 202, 81–101 (2019). https://doi.org/10.1007/s10711-018-0404-8

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