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Results tagged with equivariant-cohomology
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user 69190
2
votes
0
answers
138
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The support of a module over a equivariant cohomology ring $H^*_G$ is naturally a subset of ...
Reference: M. Atiyah, R. Bott, "The moment map and equivariant cohomology," Topology 23 (1984) (Page 5)
Let $G= T$ be a torus of dimension $l$. You may assume $G=(\mathbb C^*)^{l}$. Then the equivari …
- 2,789
5
votes
1
answer
186
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Intuition for the construction of the space $M_G=EG\times _G M$
Reference: Atiyah & Bott, The moment map and Equivariant cohomology
Question: What could be the motivation and the intuition behind the construction of the space $M_G=EG\times _G M$? When I am studyi …
- 2,789
8
votes
1
answer
801
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Chern-Weil homomorphism and classifying space
Let $G$ be a real or complex Lie group with Lie algebra $\mathfrak g$, and let $\mathbb C[\mathfrak g]$ be the algebra of $\mathbb C$-valued polynomials on $\mathfrak g$. Denote by $$\mathbb C[\mathfr …
- 2,789
7
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0
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245
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Does the Hodge decomposition hold for equivariant differential forms?
Let $M$ be a Riemannian manifold. The Hodge decomposition tells that
$$
\Omega^*(M) = \mathrm{im} \ d \oplus \mathrm{im} \ d^* \oplus \mathscr H^*(M)
$$
where $d^*$ is the adjoint operator of the ext …
- 2,789