Peripheral polynomials of hyperbolic knots. (English) Zbl 1076.57012
Let \(K\) be a hyperbolic knot in the oriented 3-sphere. Let \(X(K)\) be the character variety of representations of \(\pi_1(S^3\setminus K)\) into \(\text{SL}(2,\mathbb{C})\).
A component of \(X(K)\) containing one holonomy of the complete hyperbolic structure of finite volume on \(S^3\setminus K\) is an algebraic curve.
The paper is devoted to the study of this curve and of a family of associated polynomials.
A component of \(X(K)\) containing one holonomy of the complete hyperbolic structure of finite volume on \(S^3\setminus K\) is an algebraic curve.
The paper is devoted to the study of this curve and of a family of associated polynomials.
Reviewer: Alexandru Dimca (Nice)
MSC:
| 57M27 | Invariants of knots and \(3\)-manifolds (MSC2010) |
| 14Q05 | Computational aspects of algebraic curves |
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