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

2013/01/01 by Fumikazu Nagasato, Nagasato, Fumikazu, Anh T. Tran +1
Mathematics · #57M27 #Advanced Combinatorial Mathematics #FOS: Mathematics #Geometric Topology (math.GT) #Geometric and Algebraic Topology #Homotopy and Cohomology in Algebraic Topology #math.GT #msc:57M27

paper · pdf · doi:10.48550/arxiv.1301.0138

Title changed, 12 pages

openalex publication_date 2013/01/01 · arxiv created 2014/09/02 · arxiv updated 2014/09/03 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

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