Representations of the (-2,3,7)-Pretzel Knot and Orderability of Dehn Surgeries

Konstantinos Varvarezos

doi:10.1016/j.topol.2021.107654

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arXiv · 1911.11745

Representations of the (-2,3,7)-Pretzel Knot and Orderability of Dehn Surgeries

Konstantinos Varvarezos

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Abstract

We construct a 1-parameter family of $\mathrm{SL}_2(\mathbf{R})$ representations of the pretzel knot $P(-2,3,7)$. As a consequence, we conclude that Dehn surgeries on this knot are left-orderable for all rational surgery slopes less than 6. Furthermore, we discuss a family of knots and exhibit similar orderability results for a few other examples.

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BibTeX RIS

Konstantinos Varvarezos. 2019-11-26. Representations of the (-2,3,7)-Pretzel Knot and Orderability of Dehn Surgeries. https://doi.org/10.1016/j.topol.2021.107654

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