1998/04/30 by Lee Rudolph
Mathematics · #math.GT #msc:57M25 #msc:32S55 #msc:14H99
published as Geom. Topol. Monogr. 2 (1999), 555-562 · 8 pages. Published copy, also available at http://www.maths.warwick.ac.uk/gt/GTMon2/paper25.abs.html
arxiv created 1999/11/21 · arxiv updated 2009/11/30
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.