Mathematical Research Letters
Volume 22 (2015)
The A-polynomial and holonomy perturbations
Pages: 1401 – 1416
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.