Reidemeister-Schreier's Algorithm For 2-Coverings of Seifert Manilfolds

TL;DR

This paper presents concise formulas for applying Reidemeister-Schreier's algorithm to find all index 2 subgroups of the fundamental group of Seifert manifolds, streamlining the process of understanding their coverings.

Contribution

It introduces simplified formulas that cover all cases for 2-coverings of Seifert manifolds, improving upon classical methods.

Findings

Formulas for all cases of 2-coverings

Streamlined process for subgroup presentations

Enhanced understanding of Seifert manifold coverings

Abstract

It is classical that given any Seifert structure on N, Reidemeister-Schreier's algorithm produces a presentation of all index 2 subgroups of the fundamental group of N, described as the fundamental group of some Seifert manifolds. The new result of this article is concise formulas that gather all possible cases.