Some minimal elements for a partial order of prime knots

2014/12/10 by Teruaki Kitano, Kitano, Teruaki, Masaaki Suzuki +1
Computer Science · Mathematics · #57M27 #FOS: Mathematics #Geometric Topology (math.GT) #Geometric and Algebraic Topology #Homotopy and Cohomology in Algebraic Topology #math.GT #msc:57M27 #semigroups and automata theory

paper · pdf · doi:10.48550/arxiv.1412.3168

3 pages

openalex publication_date 2014/12/10 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

A partial order on the set of prime knots can be defined by the existence of an epimorphism between knot groups. We prove that all the prime knots with up to 6 crossings are minimal. We also show that each fibered knot with the irreducible Alexander polynomial is minimal.

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