Genera of two-bridge knots and epimorphisms of their knot groups

2017/07/12 by Masaaki Suzuki, Suzuki, Masaaki, Anh T. Tran +1
Computer Science · Mathematics · #57M25 #57M27 #FOS: Mathematics #Geometric Topology (math.GT) #Geometric and Algebraic Topology #Homotopy and Cohomology in Algebraic Topology #semigroups and automata theory

paper · pdf · doi:10.48550/arxiv.1707.03592

openalex publication_date 2017/07/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let K,K' be two-bridge knots of genus n,k respectively. We show the necessary and sufficient condition of n in terms of k that there exists an epimorphism from the knot group of K onto that of K'.

Related

• Generating function on epimorphisms between 2-bridge knot groups
• Knot Group Epimorphisms, II
• Parabolic generating pairs of genus-one 2-bridge knot groups
• A note on Riley polynomials of 2-bridge knots
• Crosscap number and epimorphisms of two-bridge knot groups