# Questions tagged [equivariant-cohomology]

The tag has no usage guidance.

28 questions
0answers
20 views

1answer
37 views

### What are some good references to learn about equivariant homotopy theory?

What are some good references to learn the foundations of equivariant homotopy theory/algebraic topology, for someone who has a background in basic homotopy theory and a tad more advanced algebraic ...
0answers
14 views

### Reference for the Cartan Model for Equivariant Cohomology

I would like references for the Cartan Model for Equivariant Cohomology which does not use supergeometry (like in the book by Berline, Getzler and Vergne). Thanks in advance.
1answer
92 views

### What is meant by the symbol $\mathbb{R}^2_{\hbar}$?

I am reading some papers in mathematical physics (https://arxiv.org/pdf/1006.0977.pdf) and I came across the following symbol $\mathbb{R}^2_{\hbar}$ I don't recognize nor could I find any background ...
0answers
52 views

### Reference Request: Spectral Sequence Relating Bredon and Borel Equivariant Cohomology.

Given a compact Lie group $G$ and a $G$-space $X$, useful invariants may obtained by studying the equivariant cohomology of $X$. There are various equivariant cohomology theories that may be defined, ...
1answer
153 views

### Interpretation of Borel equivariant cohomology.

This question should have a good answer somewhere on here, but as of yet I've been unable to find one. Any links to existing writings would be very welcome. My question relates to how exactly one ...
0answers
10 views

### Reference request: Representability of multiplicative equivariant cohomology theories

Let $G$ be a topological group, say a compact Lie group, and $e^*_G$ a multiplicative $\mathbb Z$-graded $G$-equivariant cohomology theory defined on $G$–CW complexes. Is there some analogue result to ...
0answers
38 views

### UCT for equivariant cohomology

I use the definition of Steenrod's equivariant cohomology given in chapter V of the book N. E. Steenrod. Cohomology Operations. No. 50 in Annals of Mathematics Studies. Princeton University Press, ...
0answers
59 views

1answer
106 views

### Equivariant Cohomology of homotopy equivalent spaces

Let $V$ is contractible space with $T$ torus action, then can I say their equivariant cohomology (in Borel sense) are equal ? i.e for $\bullet = point$ , $H_T^*(V)=H_T^*(\bullet)$ ?
1answer
111 views

### $Z_2$ Equivariant K-theory of $S^1$

I am interested in the $\mathbf{Z}_2$ equivariant K-theory of $S^1$, but I cannot find any good references or methods to calculate it with the action I have in mind. The action on $S^1$ is an ...
1answer
113 views

### ordinary cohomology from equvariant cohomology

Is it possible that the ordinary cohomology of a space can be obtained from its equivariant cohomology? action is algebraic torus action and space is nonsingular complete complex algebraic variety ...
1answer
134 views

### Proving one version of equivariant formality

Let $G$ be a compact, connected Lie group acting smoothly on a compact, connected and oriented smooth manifold $M$. We denote by $H_G^*(M)$ the corresponding equivariant cohomology. We have a ...
1answer
454 views

### Explanation for a line from a MathOverflow answer

Sometimes I see questions answered on MathOverflow in such a way that I don't really understand the answers. Sometimes I work out what they mean, and other times I can't. I'd like to ask for more ...