Questions tagged [equivariant-cohomology]
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179
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Equivariant KR-theory of representation sphere
I would like to say my question first.
Let $G$ be a compact Lie group acting on a good space $X$ in a good way. Let $V$ be a $G$-representation whose real dimension may be less than 8, and let $S^V$ ...
- 1,030
4
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3
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246
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Equivariant cohomology of fixed points using the localisation theorem
I am trying to understand the Smith-Thom inequality for spaces equipped with an action by a cyclic group and also the case, when it's an equality:
In the following, let $G=\mathbb{Z}/p$, $\mathbb{F}$ ...
- 41
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0
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77
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Integral equivariant formality for Hamiltonian T-actions
What is the simplest example of a compact symplectic manifold $M$ with Hamiltonian $T$-action for which the integral $T$-equivariant cohomology is not formal
i.e. $$H_T^*(M,\mathbb{Z}) \not \cong H^*(...
- 757
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1
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About Čech cohomology in transformation groups
I'm starting a study about theory of transformation groups and equivariant cohomology, in what I read several times that Čech cohomology is the most compatible with this theory, but until now I haven'...
- 237
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Cohomology of equivariant toric vector bundles using Klyachko's filtration
I am trying to understand Klyachko's following description of the cohomology groups of locally free (hopefully more generally of reflexive) sheaves on toric varieties.
Whereas detailed literature ...
- 455
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Are the spaces BG for compact connected groups G ind-projective or ind-Kähler?
Let $G$ be a compact connected group, or maybe better its complexification. By thinking about the simplicial Borel space, or using $n$-acyclic $G$-spaces for higher and higher $n$, it's "easy&...
- 44.3k
3
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Recover the $C_k$-action of a cyclic object as from the $S^1$-action on Hochschild chain
$\newcommand{\Fun}{\operatorname{Fun}}$Let $X\in\Fun(\Lambda^\mathrm{op}, \mathcal{C})$ be a cyclic object in the ($\infty$-)symmetric monoidal category $\mathcal{C}$, where $\Lambda$ is the cyclic ...
- 121
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Equivariant $K$-theory and proper actions of discrete groups
The work of Lück and Oliver describes the generalization of equivariant $K$-theory to infinite discrete groups. When $X$ is a finite proper $G$-CW complex, there exist Bott isomorphisms $K^n_G(X)\cong ...
- 21
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Is anything known about the equivariant homotopy theory of surfaces with the action of a finite subgroup of the mapping class group?
The Nielson realization theorem for a surface says that every finite subgroup of the mapping class group is realized by a finite subgroup of homeomorphisms on the surface. Furthermore, for a genus $g \...
- 61
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Equivalent descriptions of equivariant K-theory
I am looking at references for computing $$K_{T}(G/H)$$ where $G$ is a compact connected Lie group with maximal torus $T$, and $H\subset G$ is a corank one Lie subgroup such that $G/H\cong S^{2k-1}$ ...
- 51
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What is $H^*(\mathbb{CP}^{2^N-1}/\Sigma_n;\mathbb{Z})$ when $N=\binom{n}{2}$?
$H^*((S^3)^N/\Sigma_n;\mathbb{Q})$ is computed here.
It makes a little more sense to compute $H^*((S^2)^N/\Sigma_n;\mathbb{Q})$ given that global phase is irrelevant. The proof is exactly the same.
...
- 541
4
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1
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Mackey coset decomposition formula
I have a question about following argument I found
in these notes on Mackey functors:
(2.1) LEMMA. (page 6) Let $G$ be a finite group and $J$ any subgroup. Whenever $H$ and $K$ are subgroups of $J$, ...
- 5,780
2
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Torsion equivariant cohomology of reductive groups
Let $G$ be a reductive group with maximal torus $T$. One knows that the equivariant cohomology ring of a point with rational coefficients is $\mathbb{Q}[X^*(T)]^W$, and also there is an equivariant ...
- 125
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Representation-theoretic interpretation of double Schur polynomials
The Schur polynomials
$$s_\lambda(x_1, \ldots, x_n) = \frac{|x_i^{\lambda_j+n-j}|_{1\le i,j\le n}}{|x_i^{n-j}|_{1\le i,j\le n}}$$
naturally appear as polynomial representatives for Schubert classes in ...
- 3,084
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Canonical reference for dictionary between $G$-spaces and fiber bundles over $BG$?
I'm looking for a comprehensive reference (for citation purposes) laying out the basic facts of the equivalence between $G$-spaces and bundles over $BG$ for a discrete group $G$. I'd like it to also ...
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