Gonality and genus of canonical components of character varieties

Kathleen L. Petersen; Alan W. Reid

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arXiv · 1408.3665

Gonality and genus of canonical components of character varieties

Kathleen L. Petersen·Alan W. Reid

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Abstract

Let M be a two cusped hyperbolic 3-manifold and let M(r) be the result of r Dehn filling of a fixed cusp of M. We study canonical components of the SL(2,C) character varieties of M(r). We show that the gonality of these sets is bounded, independent of the filling parameter. We also obtain bounds, depending on r, for the genus of these sets. We compute the gonality for the double twist knots, demonstrating canonical components with arbitrarily large gonality.

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Kathleen L. Petersen, Alan W. Reid. 2014-08-15. Gonality and genus of canonical components of character varieties. https://arxiv.org/abs/1408.3665

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