Two-parabolic-generator subgroups of hyperbolic 3-manifold groups

TL;DR

This paper discusses Agol's theorem on two-meridional-generator subgroups of hyperbolic 2-bridge link groups and generalizes it to two-parabolic-generator subgroups of hyperbolic 3-manifold groups, refining previous results.

Contribution

It provides a detailed account of Agol's theorem and extends it to a broader class of hyperbolic 3-manifold groups, offering new insights into their subgroup structures.

Findings

Detailed account of Agol's theorem on 2-bridge link groups

Generalization to 3-manifold groups with parabolic generators

Refinement of Boileau-Weidmann's results

Abstract

We give a detailed account of Agol's theorem and his proof concerning two-meridional-generator subgroups of hyperbolic 2-bridge link groups, which is included in the slide of his talk at the Bolyai conference 2001. We also give a generalization of the theorem to two-parabolic-generator subgroups of hyperbolic 3-manifold groups, which gives a refinement of a result due to Boileau-Weidmann.