Applying TQFT to count regular coverings of Seifert 3-manifolds

TL;DR

This paper presents a formula leveraging 3D TQFT with finite gauge groups to count regular coverings of Seifert 3-manifolds, providing a new computational approach in geometric topology.

Contribution

It introduces a novel formula using 3D TQFT techniques to compute regular coverings of Seifert 3-manifolds for any finite group.

Findings

Provides a cut-and-glue method for counting coverings

Connects TQFT with topological enumeration problems

Offers explicit formulas for various finite groups

Abstract

I give a formula for computing the number of regular $\Gamma$-coverings of closed orientable Seifert 3-manifolds, for a given finite group $\Gamma$. The number is computed using a 3d TQFT with finite gauge group, through a cut-and-glue process.