On the structure of surface pure braid groups. (Q5907052)

The authors describe some of the properties of pure braid groups of surfaces different from \(\mathbb{S}^2\) and \(\mathbb{R} P^2\). In the case of compact, connected, orientable surfaces without boundary and of genus at least two, the authors give a necessary and sufficient condition for the splitting of the pure braid group exact sequence of Fadell and Neuwirth, thus answering a question of Birman.