Mathematical Research Letters

Volume 22 (2015)

Number 5

The A-polynomial and holonomy perturbations

Pages: 1401 – 1416

DOI: http://dx.doi.org/10.4310/MRL.2015.v22.n5.a7

Author

Jianfeng Lin (Department of Mathematics, University of California at Los Angeles)

Abstract

Dunfield–Garoufalidis and Boyer–Zhang proved that the A-polynomial of a non-trivial knot in $S^3$ is non-trivial. In this paper, we use holonomy perturbations to prove the non-triviality of the A-polynomial for a non-trivial, null-homotopic knot in an irreducible 3-manifold. Also, we give a strong constraint on the A-polynomial of a knot in the 3-sphere.

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