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Results tagged with equivariant-cohomology
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user 318
11
votes
What is the circle-equivariant cohomology of the real projective plane
I think one gets
$$H^*_{S^1}(\mathbb{RP}^2; \mathbb{F}_2) = \mathbb{F}_2[x, y]/(xy) $$
where $|x|=1$ and $|y|=2$. The module structure over $H^*_{S^1}(pt; \mathbb{F}_2) = \mathbb{F}_2[t]$ is given by …
- 18.2k
5
votes
Borel constructions, equivariant cohomology, and homotopy quotients of monoid actions.
This probably depends on your definition of homotopy colimit, but it you mean ``the geometric realisation of the simplicial replacement" then it seems to me that $X /\ \!/_h M$ is homeomorphic to $X \ …
- 18.2k
7
votes
Accepted
Is there a kind of Poincare duality for Borel equivariant cohomology?
This kind of thing shows up quite naturally in parameterised stable homotopy theory. Let me translate an idea I know from there into the language in this question.
Cap product gives a map
$$C^{p}(M …
- 18.2k