Addendum to: Guts, Volume and Skein Modules of 3-Manifolds

TL;DR

This paper extends previous work linking the twist number of hyperbolic links to polynomial invariants, providing a broader class of links for which volume bounds can be derived from polynomial data.

Contribution

It generalizes the proof to include a larger class of links, enhancing the applicability of polynomial invariants in estimating hyperbolic volume.

Findings

The twist number can be recovered from a Jones-like polynomial.

Polynomial invariants provide lower bounds for hyperbolic volume.

The method applies to a broader class of links than previously established.

Abstract

In Guts, Volume and Skein Modules of 3-Manifolds (arXiv:2010.06559), we showed that the twist number of certain hyperbolic weakly generalized alternating links can be recovered from a Jones-like polynomial, and offers a lower bound for the volume of the link complement. Here, we modify the proof to work for a larger class of links.