Normal generators for mapping class groups

2025/04/20 by Baik, Hyungryul, Kim, Dongryul M.
#Dynamical Systems (math.DS) #FOS: Mathematics #Geometric Topology (math.GT) #Group Theory (math.GR)

paper · doi:10.48550/arxiv.2504.14759

Abstract

In this expository note, we discuss normal generators for mapping class groups of surfaces. Especially, we focus on the relation between normal generation of a mapping class with its asymptotic translation lengths on the Teichmüller space and the curve graph of the underlying surface. We also discuss several open questions.

Citations

• Comparing Teichmüller and curve graph translation lengths
• Reducible normal generators for mapping class groups are abundant
• Minimal asymptotic translation lengths on curve complexes and homology of mapping tori
• Bottlenecks for Weil-Petersson geodesics
• Random walks, WPD actions, and the Cremona group
• Normal generators for mapping class groups are abundant
• Minimal asymptotic translation lengths of Torelli groups and pure braid groups on the curve graph
• Generating mapping class groups with elements of fixed finite order
• Pseudo-Anosov mapping classes not arising from Penner's construction
• Right-angled Artin groups and finite subgraphs of curve graphs
• Lipschitz constants to curve complexes
• Hyperbolically embedded subgroups and rotating families in groups acting on hyperbolic spaces
• Minimal pseudo-Anosov translation lengths on the complex of curves
• Right-angled Artin groups and a generalized isomorphism problem for finitely generated subgroups of mapping class groups
• The lower central series and pseudo-Anosov dilatations
• Generating the surface mapping class group by two elements
• Homomorphisms from mapping class groups
• Extremal length estimates and product regions in Teichmüller space
• On the geometry and dynamics of diffeomorphisms of surfaces
• A finite set of generators for the homeotopy group of a 2-manifold
• Die Gruppe der Abbildungsklassen: Das arithmetische Feld auf Flächen

Related

• Reducible normal generators for mapping class groups are abundant
• Normal generators for mapping class groups are abundant
• Uniformly exponential growth and mapping class groups of surfaces
• Coarsely bounded generating sets for mapping class groups of infinite-type surfaces
• Minimal Generation of Mapping Class Groups: A Survey of the Orientable Case