Homomorphisms between pure mapping class groups

2024/10/24 by de Pool, Rodrigo
#FOS: Mathematics #Geometric Topology (math.GT) #Group Theory (math.GR)

paper · doi:10.48550/arxiv.2410.18796

Abstract

Let S and S' be orientable finite-type surfaces of genus g≥ 4 and g', respectively. We prove that every multitwist-preserving map between pure mapping class groups PMap(S)→ PMap(S') is induced by a multi-embedding. As an application, we classify all homomorphisms PMap(S)→ PMap(S') for g≥ 4 and g' ≤ 6⋅ 2^g-4.

Related

• Homomorphisms from mapping class groups
• Embedding mapping-class groups of orientable surfaces with one boundary component
• Constraining mapping class group homomorphisms using finite subgroups
• Low-dimensional linear representations of mapping class groups
• Generating Extended Mapping Class Groups with Two Periodic Elements