A nonextension result on the spectral metric

Details A nonextension result on the spectral metric A nonextension result on the spectral metric

2008-05-07

arxiv.org/abs/0805.1045v1

Mathematics

Symplectic Geometry

10 pages

Scientific paper

The spectral metric, defined by Schwarz and Oh using Floer-theoretical method, is a bi-invariant metric on the Hamiltonian diffeomorphism group. We show in this note that for certain symplectic manifolds, this metric can not be extended to a bi-invariant metric on the full group of symplectomorphisms. We also study the bounded isometry conjecture of Lalonde and Polterovich in the context of the spectral metric. In particular, we show that the conjecture holds for the torus with all linear symplectic forms.

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