Affiliation:
1. Math Dept., University of California, Santa Barbara, CA 93106, USA
Abstract
This paper reviews the two variable polynomial invariant of knots defined using representations of the fundamental group of the knot complement into [Formula: see text]. The slopes of the sides of the Newton polygon of this polynomial are boundary slopes of incompressible surfaces in the knot complement. The polynomial also contains information about which surgeries are cyclic, and about the shape of the cusp when the knot is hyperbolic. We prove that at least some mutants have the same polynomial, and that most untwisted doubles have non-trivial polynomial. We include several open questions.
Publisher
World Scientific Pub Co Pte Lt
Subject
Algebra and Number Theory
Cited by
38 articles.
订阅此论文施引文献
订阅此论文施引文献,注册后可以免费订阅5篇论文的施引文献,订阅后可以查看论文全部施引文献