Quasi-morphisms on the group of area-preserving diffeomorphisms of the 2-disk via braid groups

Abstract

Recently Gambaudo and Ghys proved that there exist infinitely many quasi-morphisms on the group ${\mathrm{Diff}}_{\Omega }^{\infty }(D^2,\partial D^2)$ of area-preserving diffeomorphisms of the 2-disk $D^2$. For the proof, they constructed a homomorphism from the space of quasi-morphisms on the braid group to the space of quasi-morphisms on ${\mathrm{Diff}}_{\Omega }^{\infty }(D^2,\partial D^2)$. In this paper, we study the homomorphism and prove its injectivity.

8pages. The title of the paper has been changed, to appear in Proc. Amer. Math. Soc