Non virtually solvable subgroups of mapping class groups have non\n virtually solvable representations

2018/05/03 by Asaf Hadari, Hadari, Asaf
Mathematics · #FOS: Mathematics #Finite Group Theory Research #Geometric Topology (math.GT) #Geometric and Algebraic Topology #Group Theory (math.GR)

paper · pdf · doi:10.48550/arxiv.1805.01527

openalex publication_date 2018/05/03 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let \Σ be a compact orientable surface of finite type with at least one\nboundary component. Let \Γ \≤ textupMod(\Σ) be a non virtually\nsolvable subgroup. We answer a question of Lubotzky by showing that there\nexists a finite dimensional homological representation \ρ of\n textupMod(\Σ) such that \ρ(\Γ) is not virtually solvable. We\nthen apply results of Lubotzky and Meiri to show that for any random walk on\nsuch a group the probability of landing on a power, or on an element with\ntopological entropy 0 both decrease exponentially in the length of the walk.\n

Related

• Non-realizability of some big mapping class groups
• Mapping class groups are not linear in positive characteristic
• Solvable subgroups of Out(F_n) are virtually abelian
• Incompressible solvable representations of surface groups
• Zero entropy subgroups of mapping class groups