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.
For Rob Kirby
Keywords
almost positive link, Murasugi sum,
positive link, quasipositivity, Seifert's algorithm
