High-dimensional components of \rm SL(2,ℂ)-character varieties of prime knots

2025/12/15 by Haimiao Chen, Chen, Haimiao
Mathematics · #57K10 #57K31 #Algebraic Geometry and Number Theory #Algebraic structures and combinatorial models #FOS: Mathematics #Geometric Topology (math.GT) #Geometric and Algebraic Topology

paper · pdf · doi:10.48550/arxiv.2512.13375

openalex publication_date 2025/12/15 · openalex created_date 2025/12/17 · openalex updated_date 2026/07/28

Abstract

For a prime knot K, we give sufficient conditions for the existence of a component C of the irreducible \rm SL(2,ℂ)-character variety of K with \dimC>1, and give a lower bound for \dimC. Specifically, we improve a result of Paoluzzi and Porti on Montesinos knots, and positively answer a question posed by Culler and Dunfield in 2018.

Citations

• On torsion in the Kauffman bracket skein module of 3-manifolds
• Torsion in Kauffman bracket skein module of a 4-strand Montesinos knot exterior

Related

• The \rm SL(2,ℂ)-character variety of an arborescent knot
• The \rm SL(2,ℂ)-character variety of 8₁₈
• Finiteness of a section of the SL(2,ℂ)-character variety of knot groups
• The SL(2,C)-character varieties of torus knots
• The SL(3,C)-character variety of the figure eight knot