Invariant character varieties of hyperbolic knots with symmetries

TL;DR

This paper investigates the character varieties of symmetric hyperbolic knots, focusing on how their properties differ based on whether the knots have free or periodic symmetries, including reductions modulo p.

Contribution

It provides new insights into the behavior of invariant character varieties of symmetric knots, highlighting differences based on symmetry types and their reductions.

Findings

Character varieties differ for free vs. periodic symmetries.

Reductions mod p reveal distinct behaviors.

Symmetry type influences the structure of character varieties.

Abstract

We study character varieties of symmetric knots and their reductions mod p. We observe that the varieties present a different behaviour according to whether the knots admit a free or periodic symmetry.