Computing untwisted Dijkgraaf-Witten invariants for arborescent links

TL;DR

This paper introduces a method to compute untwisted Dijkgraaf-Witten invariants for arborescent links, providing explicit formulas for certain finite groups, thereby advancing computational techniques in 3D topological quantum field theory.

Contribution

It presents a novel computational approach for untwisted Dijkgraaf-Witten invariants specifically for arborescent links, including explicit formulas for particular finite groups.

Findings

Developed a method for computing invariants of arborescent links.

Provided explicit formulas for groups of the form Z/pZ ⋊ Z/(p-1)Z.

Enhanced computational tools in 3D topological quantum field theory.

Abstract

We briefly review 3-dimensional untwisted Dijkgraaf-Witten theory over a finite group $\Gamma$, and present a method of computing untwisted Dijkgraaf-Witten invariants for arborescent links. Some explicit formulas are given when $\Gamma=\mathbb{Z}/p\mathbb{Z}\rtimes\mathbb{Z}/(p-1)\mathbb{Z}$ for an odd prime $p$.