All Questions
Tagged with equivariant reference-request
17 questions
4
votes
0
answers
135
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Pushforward of invariant measures (equivariant Moser theorem)
There is a well-known theorem that between any two absolutely continuous Borel probability measures $\mu$ and $\nu$ on $\mathbb{R}^n$ there is an increasing triangular
transformation $T : \mathbb{R}^n ...
- 41
2
votes
1
answer
163
views
Approximation of $C^1$-smooth equivariant maps by infinitely smooth ones
Let $M,N$ be smooth closed manifolds acted by a finite group $G$. Let $f\colon M\to N$ be a $C^1$-smooth $G$-equivariant map.
Is it true that for any $\varepsilon>0$ there exists a $C^\infty$-...
- 21.8k
3
votes
0
answers
69
views
Equivariant smooth approximation
Suppose we have a compact manifold $M$ with the action of a compact group $G$. Consider the space of $C^l$ $G$-equivariant diffeomorphisms $\text{Diff}_G^{l}(M)$ with the $C^l$ topology and the space ...
- 755
6
votes
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245
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A group action on another group action quotient: how to best describe the resulting structure and does it have a name?
Suppose I have an action $\alpha:G\times X\to X$ of a group $G$ on a set $X$ and, on top of that, an action $\beta:H\times(X/G)\to(X/G)$ of another group $H$ on the set of $G$-orbits.
Is there a nice ...
- 18.4k
6
votes
0
answers
237
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Fundamental class in equivariant K-theory
I'm looking for an accessible reference for the definition of the fundamental class in equivariant K-theory.
The setup I'm interested in is the following: suppose $V$ is a vector space equipped with ...
- 371
5
votes
2
answers
1k
views
Classification of (complex algebraic) vector bundles on punctured affine space
The Quillen-Suslin theorem asserts that there are no nontrivial vector bundles over the affine space $\mathbb{A}^{n+1}$, $n\geq 0$.
Let's work over the complex numbers. What can be said about vector ...
- 23.4k
5
votes
0
answers
77
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Equivariant corner straightening
Equivariant corner straightening is usually mentioned in the literature without further explanation. What would be a reference where this is done (more or less) carefully for compact Lie group actions ...
- 29.1k
3
votes
0
answers
662
views
Equivariant Riemann-Roch on DM stacks?
Does an equivariant version of (Toen)-Riemann-Roch theorem hold say over a smooth Deligne-Mumford stack $X$ over the complex numbers?
Any references that state this explicitely?
Are there formulas ...
- 23.4k
5
votes
2
answers
1k
views
Atiyah-Guillemin-Sternberg convexity theorem
I would like to study the Atiyah-Guillemin-Sternberg convexity theorem: proof and applications. I am already familiarised with hamiltonian actions, moment maps...and with elementary Morse theory.
So ...
- 442
4
votes
1
answer
182
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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)...
- 18.9k
4
votes
2
answers
522
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Equivariant K-theory of $S^1$-action on $S^2$
Is there any references for the structure of the equivariant K-theory $K_{S^1}(S^2)$ where the action of $S^1$ on $S^2$ is defined to be rotation about the $z$-axis? What is the ring structore of $K_{...
- 9,019
2
votes
2
answers
1k
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Reference for equivariant Riemann-Roch formula?
Is there any reference for equivariant Riemann-Roch formula: book, paper, notes or something? I want to compute the weight of the action of C^* on the top wedge of cohomology group.
- 23
18
votes
8
answers
3k
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Reference request: Equivariant Topology
I am teaching a graduate seminar in equivariant topology. The format of the course is that I will give 2-3 weeks of background lectures, then each week a student will present a topic. The students ...
3
votes
1
answer
284
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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 ...
- 16.9k
21
votes
3
answers
2k
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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 ...
- 6,162
4
votes
0
answers
243
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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 $...
- 13.2k
1
vote
0
answers
182
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G-Modules on X=G/H modules on X/H ?
I think it is true that $G$-equivariant sheaves on $X$ are equal to $G/H$ equivariant sheaves on $X/H$. More precisely I'm interested in the following statement:
Given an algebraic group $G$ with ...
- 13.2k