Knot Groups with Many Killers

2009/09/17 by Daniel S. Silver, Silver, Daniel S., Wilbur Whitten +3
Computer Science · Mathematics · #20E34 #57M25 #FOS: Mathematics #Geometric Topology (math.GT) #Geometric and Algebraic Topology #Logic, programming, and type systems #semigroups and automata theory

paper · pdf · doi:10.48550/arxiv.0909.3275

openalex publication_date 2009/09/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

The group of any nontrivial torus knot, hyperbolic 2-bridge knot, or hyperbolic knot with unknotting number one contains infinitely many elements, none the automorphic image of another, such that each normally generates the group.

Citations

• Simon's conjecture for 2-bridge knots

Related

• On killers of cable knots groups
• Determining knot groups by finite quotients
• Generating pairs of 2-bridge knot groups
• Parabolic generating pairs of genus-one 2-bridge knot groups
• A New Knot Invariant