Determinants of twisted generalized hybrid weaving knots

TL;DR

This paper derives a formula for the determinant of a specific class of twisted generalized hybrid weaving knots, confirming a previous conjecture and advancing understanding of their algebraic properties.

Contribution

It provides a new explicit formula for the determinant of twisted generalized hybrid weaving knots, confirming a prior conjecture.

Findings

Derived a formula for the determinant of $ hat{Q}_3(m_1,m_2,n,l)$

Proved Conjecture 2 of Singh & Chbili (2022)

Enhanced understanding of algebraic invariants of these knots

Abstract

This article presents a formula for the determinant of the twisted generalized hybrid weaving knot $\hat{Q}_3(m_1,m_2,n,l)$, which is a closed 3-braid. As a corollary, we prove Conjecture 2 of Singh & Chbili [Nuclear Physics B, 980:115800 (2022)].