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The moment map and equivariant cohomology with generalized coefficients. (English) Zbl 0941.37050

Summary: Let \(M\) be a symplectic manifold acted on by a compact Lie group \(G\) in a Hamiltonian fashion, with proper moment map. In this situation the author introduces a pushforward morphism \({\mathcal P}:{\mathcal H}^*_G(M)\to{\mathcal M}^{-\infty}({\mathfrak g}^*)^G\), from the equivariant cohomology of \(M\) to the space of \(G\)-invariant distributions on \({\mathfrak g}^*\), which gives rise to symplectic invariants, in particular the pushforward of the Liouville measure. For the study of this pushforward morphism he makes an intensive use of equivariant forms with generalized coefficients.

MSC:

37K65 Hamiltonian systems on groups of diffeomorphisms and on manifolds of mappings and metrics
37J05 Relations of dynamical systems with symplectic geometry and topology (MSC2010)
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