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- W1640056927 abstract "Let Sigma_g be a closed orientable surface let Diff_0(Sigma_g; area) be the identity component of the group of area-preserving diffeomorphisms of Sigma_g. In this work we present an extension of Gambaudo-Ghys construction to the case of a closed hyperbolic surface Sigma_g, i.e. we show that every non-trivial homogeneous quasi-morphism on the braid group on n strings of Sigma_g defines a non-trivial homogeneous quasi-morphism on the group Diff_0(Sigma_g; area). As a consequence we give another proof of the fact that the space of homogeneous quasi-morphisms on Diff_0(Sigma_g; area) is infinite dimensional. Let Ham(Sigma_g) be the group of Hamiltonian diffeomorphisms of Sigma_g. As an application of the above construction we construct two injective homomorphisms from Z^m to Ham(Sigma_g), which are bi-Lipschitz with respect to the word metric on Z^m and the autonomous and fragmentation metrics on Ham(Sigma_g). In addition, we construct a new infinite family of Calabi quasi-morphisms on Ham(Sigma_g)." @default.
- W1640056927 created "2016-06-24" @default.
- W1640056927 creator A5090500656 @default.
- W1640056927 date "2013-06-14" @default.
- W1640056927 modified "2023-09-27" @default.
- W1640056927 title "Bi-invariant metrics and quasi-morphisms on groups of Hamiltonian diffeomorphisms of surfaces" @default.
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