Inserted: 19 aug 2020
Last Updated: 10 jan 2022
Journal: Bulletin of the London Mathematical Society
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.