Pseudo-Anosov subgroups of general fibered 3-manifold groups

TL;DR

This paper proves that certain pseudo-Anosov subgroups of fibered 3-manifold groups are convex cocompact in the mapping class group, extending known results through a combination of geometric and group-theoretic methods.

Contribution

It establishes convex cocompactness of finitely generated, purely pseudo-Anosov subgroups of fibered 3-manifold groups with reducible monodromy in the mapping class group.

Findings

Finitely generated, purely pseudo-Anosov subgroups are convex cocompact.

Results extend to all such fibered 3-manifold groups in the mapping class group.

Combines geometric group theory with fibered 3-manifold topology.

Abstract

We show that finitely generated and purely pseudo-Anosov subgroups of fibered 3-manifolds with reducible monodromy are convex cocompact as subgroups of the mapping class group via the Birman exact sequence. Combined with results of Dowdall--Kent--Leininger and Kent--Leininger--Schleimer, this establishes the result for the image of all such fibered 3-manifold groups in the mapping class group.