In differential geometry, the Kirwan map, introduced by British mathematician Frances Kirwan, is the homomorphism H G ∗ ( M ) → H ∗ ( M / / p G ) {\displaystyle H_{G}^{*}(M)\to H^{*}(M/\! /_{p}G)} where M {\displaystyle M} is a Hamiltonian G-space; i.e., a symplectic manifold acted by a Lie group G with a moment map μ : M → g ∗ {\displaystyle \mu :M\to {\mathfrak {g}}^{*}} . H G ∗ ( M ) {\displaystyle H_{G}^{*}(M)} is the equivariant cohomology ring of M {\displaystyle M} ; i.e..
In differential geometry, the Kirwan map, introduced by British mathematician Frances Kirwan, is the homomorphism H G ∗ ( M ) → H ∗ ( M / / p G ) {\displaystyle H_{G}^{*}(M)\to H^{*}(M/\! /_{p}G)} where M {\displaystyle M} is a Hamiltonian G-space; i.e., a symplectic manifold acted by a Lie group G with a moment map μ : M → g ∗ {\displaystyle \mu :M\to {\mathfrak {g}}^{*}} . H G ∗ ( M ) {\displaystyle H_{G}^{*}(M)} is the equivariant cohomology ring of M {\displaystyle M} ; i.e..
Source: Wikipedia "Kirwan map" · CC BY-SA 4.0
Share this article: X · Bluesky