Twisted Alexander Polynomials of $(-2,3,2n+1)$-Pretzel Knots

TL;DR

This paper computes the twisted Alexander polynomials for a family of pretzel knots using holonomy representations, providing evidence that these polynomials determine key knot properties like genus and fiberedness.

Contribution

It introduces explicit calculations of twisted Alexander polynomials for $(-2,3,2n+1)$-pretzel knots, supporting a conjecture relating these polynomials to knot genus and fiberedness.

Findings

Twisted Alexander polynomials are computed explicitly for the specified pretzel knots.

Results support the conjecture linking twisted Alexander polynomials to knot genus and fiberedness.

Provides new evidence for the role of holonomy representations in knot invariants.

Abstract

We calculate the twisted Alexander polynomials of $(-2,3,2n+1)$-pretzel knots associated to their holonomy representations. As a corollary, we obtain new supporting evidences of Dunfield, Friedl and Jackson's conjecture, that is, the twisted Alexander polynomials of hyperbolic knots associated to their holonomy representations determine the genus and fiberedness of the knots.