On finite quotients of surface braid groups having order at most 127

2025/12/21 by Francesco Polizzi, Polizzi, Francesco, Pietro Sabatino +1
Mathematics · #Geometric and Algebraic Topology #Algebraic Geometry and Number Theory #Homotopy and Cohomology in Algebraic Topology

paper · doi:10.48550/arxiv.2512.18817

Abstract

Let Σ_b be a compact Riemann surface of genus b ≥ 2 and let P₂(Σ_b)=π₁(Σ_b × Σ_b - Δ) be the corresponding pure braid group on two strands. A finite quotient φ\colon P₂(Σ_b) → G is called "admissible" if φ does not factor through π₁(Σ_b × Σ_b). In this work we classify all admissible quotients of P₂(Σ_b) such that |G| ≤ 127.

Citations

• Groups of order 64 and non-homeomorphic double Kodaira fibrations with the same biregular invariants
• Double Kodaira fibrations with small signature
• Kodaira fibrations and beyond: methods for moduli theory
• Compact moduli for certain Kodaira fibrations
• On residual properties of pure braid groups of closed surfaces
• Double Kodaira fibrations
• On presentation of Surface Braid Groups

Related

• Finite quotients of full surface braid groups and complex surfaces of general type: cyclic, dihedral, and extra-special quotients
• Coxeter-type quotients of surface braid groups
• Surjective homomorphisms between surface braid groups
• Intermediate subgroups of braid groups are not bi-orderable
• Abelian and metabelian quotients of surface braid groups