The index of a subgroup $H$ in a group $G$ is the number of left cosets of $H$ in G, or equivalently, the number of right cosets of $H$ in $G$. The index is denoted $(G:H).$ Let $S$ be a surface.
If $S$ is neither the sphere nor the projective plane, then what is $(B_{k}(S):PB_{k}(S))?$
Here $B_{k}(S)$ and $PB_{k}(S)$ are braid group and pure braid group of $S.$ Does anybody have a reference of $(B_{k}(S):PB_{k}(S))?$
