A Hofer-like metric on the group of symplectic diffeomorphisms

Details A Hofer-like metric on the group of symplectic diffeomorphisms A Hofer-like metric on the group of symplectic diffeomorphisms

2007-11-09

arxiv.org/abs/0711.1534v2

Mathematics

Symplectic Geometry

18 pages

Scientific paper

Using a "Hodge decomposition" of symplectic isotopies on a compact symplectic manifold $(M,\omega)$, we construct a norm on the identity component in the group of all symplectic diffeomorphisms of $(M,\omega)$ whose restriction to the group $Ham(M,\omega)$ of hamiltonian diffeomorphisms is bounded from above by the Hofer norm. Moreover, $Ham(M,\omega)$ is closed in $Symp(M,\omega)$ equipped with the topology induced by the extended norm. We give an application to the $C^0$ symplectic topology. We also discuss extensions of Oh's spectral distance.

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