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

TL;DR

This paper investigates the R$_{ abla}$-property in surface pure and full braid groups over orientable surfaces, showing that most such groups possess this property with few exceptions.

Contribution

It establishes the R$_{ abla}$-property for a broad class of surface braid groups, extending understanding of their algebraic structure.

Findings

Most surface braid groups have the R$_{ abla}$-property.

Few exceptions to the R$_{ abla}$-property are identified.

The study advances knowledge of automorphism behaviors in surface braid groups.

Abstract

Let $\Sigma_{g,p}$ 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 $P_n(\Sigma_{g,p})$ as well as for the full surface braid groups $B_n(\Sigma_{g,p})$. We show that, with few exceptions, these groups have the R$_{\infty}$-property.