  Is any positive knot the closure of a positive braid? No. But if we consider
positivity in terms of the generators of the braid group due to Birman, Ko and
Lee, then the answer is yes. In this paper we prove that the same occurs when
considering homogeneity.
  In the way we prove that the plumbing of two surfaces is a BKL-homogeneous
surface if and only if both summands are BKL-homogeneous surfaces, a parallel
result to that of Rudolph involving quasipositive surfaces. BKL-homogeneous
surfaces are, in fact, a natural generalization of quasipositive surfaces.

Geometric Topology