Hopf-braid groups

In this note we define the Hopf-braid group, a group that is directly relat ed to the group of motions of n mutually distinct lines through the origin in C-2, which is better known as the braid group of the two-sphere. It is a lso related to the motion group of the Hopf link in the three-sphere. This relationship is provided by considering the link of a union of complex line s through the origin in C-2 (i.e. the intersection of the lines with the un it 3-sphere centered at the origin in C-2). Through the study of this group we also illustrate some of the connections between the field of knots and braids and that of hyperplane arrangements.