ON QUASI-MORPHISMS FROM KNOT AND BRAID INVARIANTS

Abstract

We study quasi-morphisms on the groups Pnof pure braids on n strings and on the group [Formula: see text] of compactly supported area-preserving diffeomorphisms of an open two-dimensional disk. We show that it is possible to build quasi-morphisms on Pnby 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 Pnto build quasi-morphisms on the group [Formula: see text] of diffeomorphisms of a 2-disk.