Characterization of positive links and the $s$-invariant for links

Tetsuya Abe, Keiji Tagami

Published 2014-05-16, updated 2014-12-22Version 3

We characterize positive links in terms of strong quasipositivity, homogeneity and the value of Rasmussen, Beliakova and Wehrli's $s$-invariant. We also study almost positive links, in particular, determine the $s$-invariants of almost positive links. This result suggests that all almost positive links might be strongly quasipositive. On the other hand, it implies that almost positive links are never homogeneous links.