Character varieties of even classical pretzel knots

TL;DR

This paper computes the character varieties of irreducible SL(2,C)-representations for even classical pretzel knots and details the process of deriving their A-polynomials, advancing understanding of knot invariants.

Contribution

It provides explicit descriptions of character varieties and A-polynomials for a class of pretzel knots, a novel contribution to knot theory.

Findings

Character varieties of specific pretzel knots are explicitly determined.

A-step-by-step method for computing A-polynomials is clarified.

Results enhance understanding of knot invariants and their algebraic structures.

Abstract

For each even classical pretzel knot $P(2k_1+1,2k_2+1,2k_3)$, we determine the character variety of irreducible ${\rm SL}(2,\mathbb{C})$-representations, and clarify the steps of computing its A-polynomial.