Gonality and genus of canonical components of character varieties

Petersen, Kathleen L.; Reid, Alan W.

doi:10.48550/arxiv.1408.3665

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Appendix C the Polynomials φ K And ψ K1

Introduction1

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2019

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“…We consider the ideal generated by taking the trace in Equations ( 19), ( 20), ( 21) and (22), their image by φ * , and Equation ( 23), thus a total of 9 polynomials. We then use symbolic software to look for its prime decomposition (namely, the decomposition of its radical) and we get the eleven components we described.…”

Section: Appendix C the Polynomials φ K And ψ Kmentioning

confidence: 99%

“…In the case of knots, different invariants are related or connected to character varieties. This is, for instance, the case of the A-polynomial [5], and the algebraic and geometric properties of the excellent component of a hyperbolic knot [10,15,22]. In this paper we are interested in a far less explored type of invariants, namely the finite set of odd prime numbers p for which the character variety ramifies in characteristic p.…”

Section: Introductionmentioning

confidence: 99%

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Examples of character varieties in characteristic $p$ and ramification

Paoluzzi¹,

Porti²

2019

Preprint

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We study SL2(F)-character varieties of knots over algebraically closed fields F. We give a sufficient condition in terms of the double branched cover of a 2-bridge knot (or, equivalently, of its Alexander polynomial) on the characteristic of F, an odd prime, for the SL2(F)-character variety to present ramification phenomena. Finally we provide several explicit computations of character varieties to illustrate the result, exhibiting also other types of ramification.

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Section: Appendix C the Polynomials φ K And ψ Kmentioning

confidence: 99%