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arXiv · 0711.1534

A Hofer-like metric on the group of symplectic diffeomorphisms

Augustin Banyaga
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Abstract

Using a "Hodge decomposition" of symplectic isotopies on a compact symplectic manifold $(M,ω)$, we construct a norm on the identity component in the group of all symplectic diffeomorphisms of $(M,ω)$ whose restriction to the group $Ham(M,ω)$ of hamiltonian diffeomorphisms is bounded from above by the Hofer norm. Moreover, $Ham(M,ω)$ is closed in $Symp(M,ω)$ 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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Augustin Banyaga. 2007-11-12. A Hofer-like metric on the group of symplectic diffeomorphisms. https://arxiv.org/abs/0711.1534

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