%0 Journal Article
%T The A-polynomial And Holonomy Perturbations
%A Jianfeng Lin
%J Mathematics
%D 2013
%I arXiv
%X Dunfield-Garoufalidis and Boyer-Zhang proved that the A-polynomial of a nontrivial knot in $S^{3}$ is nontrivial. In this paper, we use holonomy perturbations to prove the non-triviality of the A-polynomial for a nontrivial, 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.
%U http://arxiv.org/abs/1304.7232v2