  A differential geometric characterization of the braid-index of a link is
found. After multiplication by 2pi, it equals the infimum of the sum of total
curvature and total absolute torsion over holonomic representatives of the
link.
  Upper and lower bounds for the infimum of total curvature over holonomic
representatives of a link are given in terms of its braid- and bridge-index.
Examples showing that these bounds are sharp are constructed.
