Problems, Questions, and Conjectures about Mapping Class Groups

2018/06/22 by Dan Margalit, Margalit, Dan · 2 citations
Mathematics · #Algebraic Geometry and Number Theory #FOS: Mathematics #Geometric Topology (math.GT) #Geometric and Algebraic Topology #Homotopy and Cohomology in Algebraic Topology

paper · pdf · doi:10.48550/arxiv.1806.08773

openalex publication_date 2018/06/22 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We discuss a number of open problems about mapping class groups of surfaces. In particular, we discuss problems related to linearity, congruence subgroups, cohomology, pseudo-Anosov stretch factors, Torelli subgroups, and normal subgroups.

Citations

• Generating Mapping Class Groups by Involutions
• Torsion Elements in the Mapping Class Group of a Surface
• Small dilatation pseudo-Anosov homeomorphisms and 3-manifolds

Cited by

• Linearity criteria for automorphism groups of malabelian groups
• Finite generation of abelianizations of the genus 3 Johnson kernel and the commutator subgroup of the Torelli group for Out(F₃)

Related

• Cohomological structure of the mapping class group and beyond
• Subgroups of the mapping class group from the geometrical viewpoint
• Geometric survey of subgroups of mapping class groups
• On generating mapping class groups by pseudo-Anosov elements
• On the Subgroups of Right Angled Artin Groups and Mapping Class Groups