Communications in Analysis and Geometry

Volume 30 (2022)

Number 4

Jones slopes and coarse volume of near-alternating knots

Pages: 891 – 948


Christine Ruey Shan Lee (Department of Mathematics and Statistics, University of South Alabama, Mobile, Ala., U.S.A.)


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.

Received 22 May 2018

Accepted 12 August 2019

Published 30 January 2023