Brunnian braids on surfaces

Abstract

We determine a set of generators for the Brunnian braids on a general surface $M$ for $M\ne S^2$ or $ℝP^2$. For the case $M=S^2$ or $ℝP^2$, 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.