Kirwan map

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

H^*_G(M) \to H^*(M /\!/_p G)

where

It is defined as the map of equivariant cohomology induced by the inclusion \mu^{-1}(p) \hookrightarrow M followed by the canonical isomorphism 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.[1]

References

  1. M. Harada, G. Landweber. Surjectivity for Hamiltonian G-spaces in K-theory. Trans. Amer. Math. Soc. 359 (2007), 6001--6025.
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