  We study quasi-morphisms on the groups Pn of pure braids on n strings and on
the group D of compactly supported area-preserving diffeomorphisms of an open
two-dimensional disc. We show that it is possible to build quasi-morphisms on
Pn by using knot invariants which satisfy some special properties. In
particular, we study quasi-morphisms which come from knot Floer homology and
Khovanov-type homology. We then discuss possible variations of the
Gambaudo-Ghys construction, using the above quasi-morphisms on Pn to build
quasi-morphisms on the group D of diffeomorphisms of a 2-disc.
