Jones polynomials, volume, and essential knot surfaces: a survey

Abstract

This paper is a brief overview of recent results by the authors relating colored Jones polynomials to geometric topology. The proofs of these results appear in the papers [arXiv:1002.0256] and [arXiv:1108.3370], while this survey focuses on the main ideas and examples.

27 pages, 23 figures. v2 contains minor revisions and updated references. To appear in Proceedings of Knots in Poland III