The AJ-Conjecture for Cables of Two Bridge Knots

2014/12/02 by Nathan Druivenga, Druivenga, Nathan
Engineering · Mathematics · #Advanced Combinatorial Mathematics #Advanced Numerical Analysis Techniques #Geometric and Algebraic Topology #math.GT #msc:57M27

paper · pdf · doi:10.48550/arxiv.1412.1053

17 pages, 1 figures

arxiv created 2015/03/02 · arxiv updated 2015/03/03

Abstract

The AJ-conjecture for a knot K ⊂ S³ relates the A-polynomial and the colored Jones polynomial of K. If a two-bridge knot K satisfies the AJ-conjecture, we give sufficient conditions on K for the (r,2)-cable knot C to also satisfy the AJ-conjecture. If a reduced alternating diagram of K has η₊ positive crossings and η_- negative crossings, then C will satisfy the AJ-conjecture when (r+4η_-)(r-4η₊)>0 and the conditions of the main theorem are satisfied.

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