- 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 .
- F. C. Kirwan, Cohomology of Quotients in Complex and Algebraic Geometry, Mathematical Notes 31, Princeton University Press, Princeton N. J., 1984.
- M. Harada, G. Landweber. Surjectivity for Hamiltonian G-spaces in K-theory. Trans. Amer. Math. Soc. 359 (2007), 6001--6025.