Smooth manifolds

Kirwan map

In differential geometry, the Kirwan map, introduced by British mathematician Frances Kirwan, is the homomorphism where * is a Hamiltonian G-space; i.e., a symplectic manifold acted by a Lie group G with a moment map . * is the equivariant cohomology ring of ; i.e.. the cohomology ring of the homotopy quotient of by . * is the symplectic quotient of by at a regular central value of . It is defined as the map of equivariant cohomology induced by the inclusion followed by the canonical isomorphism . A theorem of Kirwan says that if is compact, then the map is surjective in rational coefficients. The analogous result holds between the K-theory of the symplectic quotient and the equivariant topological K-theory of . (Wikipedia).

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Related pages

Compact space | Differential geometry | Symplectic manifold | Moment map | K-theory | Homomorphism