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

Details Quasi-morphisms on the group of area-preserving diffeomorphisms of the 2-disk Quasi-morphisms on the group of area-preserving diffeomorphisms of the 2-disk

2012-04-18

arxiv.org/abs/1204.4056v1

Mathematics

Dynamical Systems

Scientific paper

Recently Gambaudo and Ghys proved that there exist infinitely many quasi-morphisms on the group ${\rm Diff}_\Omega^\infty (D^2, \partial D^2)$ 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 ${\rm Diff}_\Omega^\infty (D^2, \partial D^2)$. In this paper, we study the homomorphism and prove its injectivity.

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