The A-polynomial And Holonomy Perturbations

Abstract

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.

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

References in corpus (2)

• Dehn surgery, the fundamental group and SU(2)
• Non-triviality of the $M$-degree of the $A$-polynomial

Cited by in corpus (1)

• SU(2)-Cyclic Surgeries on Knots