Slice-torus link invariants, combinatorial invariants, and positivity conditions

Abstract

We prove some necessary conditions for a link to be: concordant to a quasi-positive link, quasi-positive, positive, or the closure of a positive braid. The main applications of our results are: a characterisation of positive links with unlinking number 1 and 2, and a combinatorial criterion to test if a positive link is the closure of a positive braid.