English

The A-polynomial And Holonomy Perturbations

Geometric Topology 2015-03-24 v2

Abstract

Dunfield-Garoufalidis and Boyer-Zhang proved that the A-polynomial of a nontrivial knot in S3S^{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.

Cite

@article{arxiv.1304.7232,
  title  = {The A-polynomial And Holonomy Perturbations},
  author = {Jianfeng Lin},
  journal= {arXiv preprint arXiv:1304.7232},
  year   = {2015}
}

Comments

12 pages, 2 figures. Typos corrected. Added Lemma 3.2

R2 v1 2026-06-22T00:07:05.715Z