Pseudo-Anosov subgroups of surface bundles over tori

2025/05/07 by Ryang, Junmo
#20E08 #20F65 #57K20 #FOS: Mathematics #Geometric Topology (math.GT) #Group Theory (math.GR)

paper · doi:10.48550/arxiv.2505.07848

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.

Citations

• Purely pseudo-Anosov subgroups of the genus two handlebody group
• Pseudo-Anosov subgroups of general fibered 3-manifold groups
• Convex-cocompact subgroups of the Goeritz group
• Undistorted purely pseudo-Anosov groups
• The geometry of purely loxodromic subgroups of right-angled Artin groups
• Pseudo-Anosov subgroups of fibered 3-manifold groups
• Uniform convergence in the mapping class group
• Trees and mapping class groups
• Right-veering diffeomorphisms of compact surfaces with boundary I
• Shadows of mapping class groups: capturing convex cocompactness
• Geometry of the complex of curves II: Hierarchical structure

Related

• Pseudo-Anosov subgroups of general fibered 3-manifold groups
• Pseudo-Anosov subgroups of fibered 3-manifold groups
• Purely pseudo-Anosov subgroups of the genus two handlebody group
• Undistorted purely pseudo-Anosov groups
• Convex-cocompact subgroups of the Goeritz group