Hyperbolicity of the canonical genus two knots. (November 2020)

• Record Type: Journal Article
• Authors: Stoimenow, A.
• Is Part Of: Journal of symbolic computation. Volume 101(2020)
• Page Start: 242
• Page End: 269
• Publication Date: 2020-11
• Subjects: primary 57M25 57M50 -- secondary 57M15 12Y05 13F20 13P15; Hyperbolic knot -- Prime knot -- Link polynomial -- Canonical genus -- Bridge number -- Vassiliev invariant; Mathematics -- Data processing -- Periodicals; Numerical analysis -- Data processing -- Periodicals; Automatic programming (Computer science) -- Periodicals; Mathématiques -- Informatique -- Périodiques; Analyse numérique -- Informatique -- Périodiques; Programmation automatique -- Périodiques; Automatic programming (Computer science); Mathematics -- Data processing; Numerical analysis -- Data processing; Periodicals; Electronic journals; 510.285
• DOI: 10.1016/j.jsc.2019.08.003
• Languages: English
• ISSNs: 0747-7171

Abstract

Abstract: We classify the non-hyperbolic knots (i.e., torus, satellite and composite knots) of canonical genus at most 2. We use cut-and-paste and combinatorial arguments, but most substantially we develop an approach for (computationally) testing knot primeness using link polynomials.