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On the AJ conjecture for cables of the figure eight knot

Authors
  • Tran, Anh T.
Type
Preprint
Publication Date
Sep 02, 2014
Submission Date
May 15, 2014
Identifiers
arXiv ID: 1405.4055
Source
arXiv
License
Yellow
External links

Abstract

The AJ conjecture relates the A-polynomial and the colored Jones polynomial of a knot in the 3-sphere. It has been verified for some classes of knots, including all torus knots, most double twist knots, (-2,3,6n \pm 1)-pretzel knots, and most cabled knots over torus knots. In this paper we study the AJ conjecture for (r,2)-cables of a knot, where r is an odd integer. In particular, we show that the AJ conjecture holds true for (r,2)-cables of the figure eight knot, where r is an odd integer satisfying |r| \ge 9.

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