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

1997/09/06 by Alexander Reznikov, Reznikov, Alexander
Mathematics · #Homotopy and Cohomology in Algebraic Topology #Geometric and Algebraic Topology #Geometry and complex manifolds

paper · pdf · doi:10.48550/arxiv.dg-ga/9709010

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.

Related

• Characteristic Classes in Symplectic Topology
• Symplectic Groups, Mapping Class Groups and the Stability of Bounded Cohomology
• Symplectomorphism groups and almost complex structures
• On the moduli space of flat symplectic surface bundles
• Lectures on Groups of Symplectomorphisms