Some families of minimal elements for the partial ordering on prime knots

Abstract

We show that all twist knots, certain double twist knots and some other 2-bridge knots are minimal elements for the partial ordering on the set of prime knots. The key to these results are presentations of their character varieties using Chebyshev polynomials and a criterion for irreducibility of a polynomial of two variables. These give us an elementary method to discuss the number of irreducible components of the character varieties, which concludes the result essentially.

Title changed, 12 pages

References in corpus (3)

• Epimorphisms between 2-bridge link groups
• On Character varieties of two-bridge knot groups
• Epimorphisms and Boundary Slopes of 2-Bridge Knots