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On the AJ conjecture for cables of twist knots

Volume 230 / 2015

Anh T. Tran Fundamenta Mathematicae 230 (2015), 291-307 MSC: Primary 57N10; Secondary 57M25. DOI: 10.4064/fm230-3-5

Abstract

We study the AJ conjecture that relates the A-polynomial and the colored Jones polynomial of a knot in $S^3$. We confirm the AJ conjecture for $(r,2)$-cables of the $m$-twist knot, for all odd integers $r$ satisfying $$\begin{cases} (r+8)(r-8m)>0 &\mbox{if } m> 0, \\ r(r+8m-4)>0 &\mbox{if } m<0. \end{cases} $$

Authors

  • Anh T. TranDepartment of Mathematical Sciences
    The University of Texas at Dallas
    Richardson, TX 75080, U.S.A.
    e-mail

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