Journal of Knot Theory and Its Ramifications · 2001 · 41 citations · 0 references
Natural SciencesMathematicsAlgebraGeometryTopologyAlgebraic GeometryArithmetic GeometryFundamental GroupGalois TheoryHyperbolic GeometryKnot TheoryCrossing NumberHyperbolic Knots
In this paper we compute the trace field for the family of hyperbolic twist knots. We describe this field as a simple extension ℚ(z 0 ) where z 0 is a specified root of a particular irreducible polynemial Φ n (z)∈ℤ[z]. As a consequence, we find that the degree of the trace field is precisely two less than the-minimal crossing number of a twist knot.