  Let S(D) be the surface produced by applying Seifert's algorithm to the
oriented link diagram D. I prove that if D has no negative crossings then S(D)
is a quasipositive Seifert surface, that is, S(D) embeds incompressibly on a
fiber surface plumbed from positive Hopf annuli. This result, combined with the
truth of the `local Thom Conjecture', has various interesting consequences; for
instance, it yields an easily-computed estimate for the slice euler
characteristic of the link L(D) (where D is arbitrary) that extends and often
improves the `slice-Bennequin inequality' for closed-braid diagrams; and it
leads to yet another proof of the chirality of positive and almost positive
knots.
