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continious cohomology of groups of volume-preserving and symplectic diffepmorphisms, measurable transfer and higher asymtotic cycles

Alexander Reznikov
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Abstract

I construct the real counterparts (which I call Borel-Bott classes) of the R/Z classes constructed in "Characteristic classes in symplectic topology", to appear, in the cohomology of volume-preserving and symplectomorhisms of a compact (symplectic) manifold.I show that, for the symplectic action of the mapping class group in the moduli space of stable vector bundles over a Riemann surface, the restriction of the first constructed class from the symplectomorphism group gives a generator for the second (bounded) cohomology of the mapping class group.

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Alexander Reznikov. 1997-09-06. continious cohomology of groups of volume-preserving and symplectic diffepmorphisms, measurable transfer and higher asymtotic cycles. https://arxiv.org/abs/dg-ga/9709010

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