Jones slopes and coarse volume of near-alternating links

Christine Ruey Shan Lee

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arXiv · 1708.04900

Jones slopes and coarse volume of near-alternating links

Christine Ruey Shan Lee

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Abstract

We study near-alternating links whose diagrams satisfy conditions generalized from the notion of semi-adequate links. We extend many of the results known for adequate knots relating their colored Jones polynomials to the topology of essential surfaces and the hyperbolic volume of their complements: we show that the Strong Slope Conjecture is true for near-alternating knots with spanning Jones surfaces, their colored Jones polynomials admit stable coefficients, and the stable coefficients provide two-sided bounds on the volume of the knot complement. We also discuss extensions of these results to their Murasugi sums and a class of highly twisted links.

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BibTeX RIS

Christine Ruey Shan Lee. 2017-08-16. Jones slopes and coarse volume of near-alternating links. https://arxiv.org/abs/1708.04900

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