Pseudo-Anosov subgroups of surface bundles over tori

TL;DR

This paper proves that certain subgroups of surface bundle groups over tori are convex cocompact in the mapping class group, extending known results from fibered 3-manifold groups.

Contribution

It generalizes the convex cocompactness property of pseudo-Anosov subgroups from fibered 3-manifolds to surface bundles over tori.

Findings

Finitely generated, purely pseudo-Anosov subgroups are convex cocompact in the mapping class group.

Extends known convex cocompactness results to a broader class of 3-manifold groups.

Connects subgroup properties with the Birman exact sequence.

Abstract

We show that finitely generated, purely pseudo-Anosov subgroups of the fundamental groups of surface bundles over tori are convex cocompact as subgroups of the mapping class group via the Birman exact sequence. This generalizes the fact that similar groups within fibered 3-manifold groups are convex cocompact, which is a combination of results due to Dowdall, Kent, Leininger, Russell, and Schleimer.