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[1] 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 .[2]
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Categories:
- Smooth manifolds
- Differential geometry stubs