# Tagged Questions

The tag has no usage guidance.

71 views

172 views

258 views

168 views

### Vector bundles on a weighted projective stack

Put $X := \mathbb A^{n+1}\!-\lbrace0\rbrace$. Let $G=\mathbb C^*$ act on $X$ with (positive) weights $w_0,\dots,w_n$. The quotient stack $[X/G]$ is called the weighted projective stack. Each vector ...
250 views

### equivariant resolution of singularities

I am looking for some references on equivariant resolution of singularities. In most references quoted on mathoverflow (for instance : Reference on an equivariant resolution of singularities), they ...
232 views

### Non-Symmetric Equivariant Riemannian Metrics on Homogeneous Spaces

For a homogeneous space $M = G/H$, the number of $H$-equivariant Riemannian metrics on $M$ is usually much smaller than the space of Riemannian metrics. I am wondering what happens when the symmetric ...
73 views

### Classifying Equivariant Maps Between Fin-Dim Irreducible Modules

Let $G$ be a compact semi-simple Lie group, (or to be even more concrete let $G = SL(N)$), and let $V$ and $W$ be finite dimensional irreducible representations of $G$. Surely it is very well-known ...
86 views

### Classifying all Equivariant Bilinear Forms on a Finite-Dimensional Module

Given a finite dimensional (real) vector space $V$, and two non-degenerate bilinear forms $(\cdot,\cdot)_1$ and $(\cdot,\cdot)_2$, one can use a basic linear algebra argument to show that there exists ...
462 views

### Weights on equivariant cohomology?

Let $X$ be a quasi-projective variety over the complex numbers, equipped with an action of a linear algebraic group $G$. Is there a natural mixed Hodge structure on its equivariant cohomology? Is ...
130 views

### Equivariant versus retractive spaces: a reference request

Let $T$ be the category of compactly generated weak Hausdorff spaces with model structure given by Serre fibrations, Serre cofibrations and weak homotopy equivalences. Let $G = |G.|$ be the (geometric)...
433 views

### What is the right notion of equivariant Cech cohomology?

What is the right definition of equivariant Cech cohomology is so that given a $G$-space $X$, $H^1_G(X;H)$ classifies $G$-equivariant principal $H$-bundles on $X$?
302 views

747 views

I'm trying to read through "The index of elliptic operators I," and here's what I understand of the structure of the proof: Define (using purely K-theoretic means) a homomorphism $K_G(TX) \to R(G)... 0answers 243 views ### Lifting of torus action to line bundle Let$\mathbb{P}(V) = \mathbb{P}(\mathbb C \oplus \mathbb C)$be with a$\mathbb C^*$action :$\lambda (u,v) = (u,\lambda v)$. There are two fixed points of this action, say$0$and$\infty$. What ... 1answer 268 views ### For a G-variety, what could one say about the motif of the corresponding simplicial variety Let G be an algerbraic group, and X be a G-variety (that I will assume to be smooth). Then one can consider a simlicial variety whose terms are$G^i\times X$. This simplicial variety yields a 'complex ... 0answers 332 views ### Equivariant sheaves and simplicial varieties I would like to proof the following theorem: Let$\pi:X\rightarrow X/G$be a principal$G$-bundle (say of varieties, Zariski locally trivial), then$\pi^*$induces an equivalence between modules on ... 0answers 1k views ### Is the equivariant cohomology an equivariant cohomology? Suppose a finite group$G$acts piecewise linearly on a polyhedron$X$. Then there are two kinds of equivariant cohomology (or homology).$\bullet$With coefficients in a$\Bbb Z G$-module$M$. A ... 1answer 774 views ### Formality of classifying spaces Let$G$be a compact Lie group (or reductive algebraic group over$\mathbb{C}$), and let$BG$be its classifying space. Fix a prime$p$. Let$\mathcal{A}$denote the dg algebra of singular cochains on ... 6answers 528 views ### Equivariant homology of$\Omega X$\/-space (references needed)? Let$(X, *)$be pointed a (1-connected) space, and let$\Omega X$denote its based loops space. Then, as one knows very well,$\Omega X$is a group up to homotopy (this includes all the necessary ... 0answers 934 views ### Why is the Nil-Hecke Algebra appearing? The Nil-Hecke algebra is defined to be the subalgebra of the endomorphism ring of$\mathbb{C}[x_1,\ldots,x_n]$generated by the operators of multiplication by$x_i$and the divided difference ... 0answers 183 views ### Equivariant sheaves basics reference I am looking for a reference for basic facts about actions of linear algebraic groups and their Lie-algebras on$\mathcal O_X$-modules. For example I could not find a reference the following: Let$...
It seems that there are two notions of strongly equivaraint $D_X$- Modules and I would like to know if they are equivalent, or at least how they are related. Let $\rho: G\times X \rightarrow X$ be an ...
### What does this naive attempt at $S^1$-equivariant homology describe?
After reading Cohen and Voronov's notes on string topology, one can find the following construction: Suppose we have a topological space $X$ with continuous action of $S^1$. This means we have a map \$\...