The R_∞-property for braid groups over orientable surfaces

2025/02/20 by Karel Dekimpe, Dekimpe, Karel, Daciberg Lima Gonçalves +3
Mathematics · #20E45 #Algebraic Geometry and Number Theory #FOS: Mathematics #Geometric Topology (math.GT) #Geometric and Algebraic Topology #Group Theory (math.GR) #Homotopy and Cohomology in Algebraic Topology #Primary: 20E36 #Secondary: 20F36

paper · pdf · doi:10.48550/arxiv.2502.14824

openalex publication_date 2025/02/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/03

Abstract

Let Σ_g,p be an orientable surface of genus g and of finite type without boundary (i.e. an orientable closed surface with a finite number p of points removed). In this paper we study the R_∞-property for the surface pure braid groups P_n(Σ_g,p) as well as for the full surface braid groups B_n(Σ_g,p). We show that, with few exceptions, these groups have the R_∞-property.

Related

• Automorphisms of surface braid groups
• Twisted conjugacy classes in Symplectic groups, Mapping class groups and Braid groups(including an Appendix written with Francois Dahmani)
• On presentation of Surface Braid Groups
• On residual properties of pure braid groups of closed surfaces
• Lower central series for surface braid groups