Magnus subgroups of one-relator surface groups

TL;DR

This paper investigates the properties of Magnus subgroups within one-relator surface groups, focusing on their intersections and conjugates, and draws parallels to classical one-relator group theory results.

Contribution

It extends classical one-relator group results to the setting of one-relator surface groups, analyzing subgroup intersections and conjugacy properties.

Findings

Results on intersections of Magnus subgroups

Analogies with classical one-relator group theory

Insights into subgroup conjugacy behavior

Abstract

A one-relator surface group is the quotient of an orientable surface group by the normal closure of a single relator. A Magnus subgroup is the fundamental group of a suitable incompressible sub-surface. A number of results are proved about the intersections of such subgroups and their conjugates, analogous to results of Bagherzadeh, Brodskii, and Collins in classical one-relator group theory.