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

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.

18 pages

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