A Jones Slopes Characterization of Adequate Knots
نویسنده
چکیده
We establish a characterization of adequate knots in terms of the degree of their colored Jones polynomial. We show that, assuming the Strong Slope conjecture, our characterization can be reformulated in terms of “Jones slopes” of knots and the essential surfaces that realize the slopes. For alternating knots the reformulated characterization follows by recent work of J. Greene and J. Howie. 2010 Mathematics Classification: 57N10, 57M25.
منابع مشابه
Slopes and Colored Jones Polynomials of Adequate Knots
Garoufalidis conjectured a relation between the boundary slopes of a knot and its colored Jones polynomials. According to the conjecture, certain boundary slopes are detected by the sequence of degrees of the colored Jones polynomials. We verify this conjecture for adequate knots, a class that vastly generalizes that of alternating knots.
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