Brunnian Braids on Surfaces

We determine a set of generators for the Brunnian braids on a general surface $M$ for $M≠S^2$ or ${\text{RP}}^2$. For the case $M=S^2$ or ${\text{RP}}^2$, a set of generators for the Brunnian braids on $M$ is given by our generating set together with the homotopy groups of a 2-sphere.