The 500 simplest hyperbolic knots
Abhijit Champanerkar, Ilya Kofman, Timothy Mullen
TL;DR
This paper classifies all hyperbolic knots with complements in a specific hyperbolic manifold census and computes their Jones polynomials, providing a comprehensive catalog of these knots.
Contribution
It identifies all hyperbolic knots with complements in the census of orientable one-cusped hyperbolic manifolds with eight ideal tetrahedra and computes their Jones polynomials.
Findings
Complete list of hyperbolic knots with eight tetrahedra complements
Computed Jones polynomials for these knots
Enhanced understanding of hyperbolic knot classification
Abstract
We identify all hyperbolic knots whose complements are in the census of orientable one-cusped hyperbolic manifolds with eight ideal tetrahedra. We also compute their Jones polynomials.
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