The R$_{\infty}$-property for braid groups over orientable surfaces

• DOI: 10.48550/arxiv.2502.14824
• Publication Date: 2025-01-01
• Authors: Dekimpe, Karel; Gonçalves, Dacibe...; Ocampo, Oscar
• Keywords: Mathematics - Geometric Topology; FOS: Mathematics; Geometric Topology (math.GT); Primary: 20E36, Secondary: 20F36, 20E45; Group Theory (math.GR); Mathematics - Group Theory

18 pages<br/>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$_{\infty}$-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$_{\infty}$-property.<br/>