Work

Two-bridge knot epimorphisms and intersections in the character variety

Year: 2026

Type: preprint

Abstract: We study the SL(2,C) character varieties of hyperbolic two-bridge knot groups admitting epimorphisms onto the trefoil knot group. Ohtsuki, Riley, and Sakuma give a systematic construction of an infinite family of such knots. The character varieties of these knot groups contain a component of irreducible representations arising from the epimorphism, which is distinct from the canonical component. We prove that every affine point of intersection between this component and any other component is algebraic non-integral, and therefore detects an essential surface in the knot complement. We also determine the boundary slope of each detected surface explicitly in terms of the continued fraction expansion of the two-bridge knot.

Source: arXiv (Cornell University)

DOI: 10.48550/arxiv.2610.23731

Authors: Bailly-Hall, Isidora, Chu, Michelle, Dovgodko, Karina, Ganguly, Akash, Kang, Jiachen, Sun, Jishi

Language: English

Topic: Geometric and Algebraic Topology

Subfield: Geometry and Topology

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

Funders: National Science Foundation, Eli Lilly and Company, University of Minnesota

Awards: RTG: Combinatorics and Algebra, CAREER: Virtual properties of groups in geometry and topology, Hyperbolic Manifolds and Their Embedded Submanifolds

OpenAlex ID: W7222972848

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