Kirwan map

In differential geometry, the Kirwan map, introduced by British mathematician Frances Kirwan, is the homomorphism

where

It is defined as the map of equivariant cohomology induced by the inclusion ${\displaystyle \mu ^{-1}(p)\hookrightarrow M}$ followed by the canonical isomorphism ${\displaystyle H_{G}^{*}(\mu ^{-1}(p))=H^{*}(M/\!/_{p}G)}$.

A theorem of Kirwan says that if M 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 M.

...
Wikipedia