  Branch points of a real 2-surface S in a 4-manifold M generalize the branch
points of complex curves in complex surfaces: for example, they can occur as
singularities of minimal surfaces. We investigate such a branch point p when S
is topologically embedded in M. It defines a link L(p), the components of which
are closed braids with the same axis up to orientation. If S is closed without
boundary, the contribution of p to the degree of the normal bundle of S in M
can be computed on the link L(p) in terms of the algebraic crossing numbers of
its components and on their linking numbers one with another.
