Abstract
We show that all twist knots and certain double twist knots are minimal elements for a partial ordering on the set of prime knots. The keys 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.
Citation
Fumikazu Nagasato. Anh T. Tran. "Some families of minimal elements for a partial ordering on prime knots." Osaka J. Math. 53 (4) 1029 - 1045, October 2016.
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