All Questions
8 questions
22
votes
3
answers
1k
views
Applications of topological and diferentiable stacks
What are some examples of theorems about topology or differential geometry that have been proven using topological/differentiable stacks, or, some examples of proofs made easier by them? I'm well ...
- 15.5k
7
votes
3
answers
813
views
Is there a "geometric" language that describes the equivalence groupoid of a foliated manifold?
Sitting on the couch in my office is a certain groupoid. It's waiting for me to say something to it. My problem is that I don't know its language. My question here is for some suggestions.
Here, ...
- 54.6k
4
votes
1
answer
247
views
unit element under map of stacks $B\mathcal{G}\rightarrow B\mathcal{H}$
Let $\mathcal{G}$ be a Lie groupoid. The target map $t:\mathcal{G}_1\rightarrow \mathcal{G}_0$ is a principal $\mathcal{G}$ bundle.
This article Orbifolds as Stacks? by Eugene Lerman calls (in page $...
- 6,023
4
votes
1
answer
334
views
Gluing together together differentiable stacks
I am trying to figure out the conditions under which you can glue together a collection of (differentiable) stacks by equivalences, and get a differentiable stack.
More precisely, I have a collection ...
- 43
4
votes
1
answer
541
views
Intrinsic Characterization of when an orbifold (or more general stack) is effective?
Recall that an orbifold is an etale and proper differentiable stack $X$. Etale means that it admits an etale atlas $M \to X$ from a manifold $M$ (which is to say it is represented by an etale Lie ...
- 15.5k
3
votes
3
answers
522
views
Lie groupoids in practice
I am familiar with the notion of Lie groupoids.
But, only easy examples of Lie groupoids I am familiar with are the following:
Lie groupoids coming from manifolds; that are of the form $(M\...
- 6,023
2
votes
2
answers
530
views
Fibered product of stacks comes from a Lie groupoid
I am adding some context here. I am reading Introduction to Differentiable Stacks by Gregory Ginot.
In page no $7$, just before the remark $2.2$ he says the following.
One shall be careful that ...
- 6,023
2
votes
1
answer
401
views
Composition of bibundles
I am reading Orbifolds as stacks?
Given Lie groupoids $\mathcal{G}$ and $\mathcal{H}$ there is a notion of what is called a bibundle from $\mathcal{G}$ to $\mathcal{H}$ which is supposed to be a ...
- 6,023