A Hofer-like metric on the group of symplectic diffeomorphisms

2007/11/09 by Banyaga, Augustin
#53D05 #53D35 #FOS: Mathematics #Symplectic Geometry (math.SG)

paper · doi:10.48550/arxiv.0711.1534

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 C⁰ symplectic topology. We also discuss extensions of Oh's spectral distance.

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