Freely 2-periodic knots have two canonical components

2024/03/11 by Keegan Boyle, Boyle, Keegan, Nicholas Rouse +1 · 1 citation
Computer Science · Mathematics · #57K10 #57K31 #57M60 #FOS: Mathematics #Geometric Topology (math.GT) #Geometric and Algebraic Topology #Mathematical Dynamics and Fractals #semigroups and automata theory

paper · pdf · doi:10.48550/arxiv.2403.07157

openalex publication_date 2024/03/11 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We prove that the SL(2, C) character variety of a hyperbolic, freely 2-periodic knot has two canonical components. We also prove that the hyperbolic torsion polynomial of such a knot satisfies a factorization condition which seems to be particularly effective at identifying freely 2-periodic knots.

Cited by

• Extending degree-2 Azumaya algebras with C2-actions and examples from character varieties of knot group

Related

• Obstructions to free periodicity and symmetric L-space knots
• Invariant character varieties of hyperbolic knots with symmetries
• The \rm SL(2,ℂ)-character variety of 8₁₈
• The \rm SL(2,ℂ)-character variety of an arborescent knot
• The SL(2,C)-character varieties of torus knots