Knot Cabling and the Degree of the Colored Jones Polynomial II

2015/01/19 by Kalfagianni, Efstratia, Tran, Anh T.
#FOS: Mathematics #Geometric Topology (math.GT) #Primary 57N10. Secondary 57M25

paper · doi:10.48550/arxiv.1501.04614

Abstract

We continue our study of the degree of the colored Jones polynomial under knot cabling started in "Knot Cabling and the Degree of the Colored Jones Polynomial" (arXiv:1501.01574). Under certain hypothesis on this degree, we determine how the Jones slopes and the linear term behave under cabling. As an application we verify Garoufalidis' Slope Conjecture and a conjecture of the authors for cables of a two-parameter family of closed 3-braids called 2-fusion knots.

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