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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, ...
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 ...
7 votes
1 answer
403 views

What is the local structure of a Lie groupoid?

A manifold is locally $\mathbb R^n$. An orbifold is locally $\mathbb R^n/\{\text{finite group}\}$. Is there a similar way to think about the local structure of a Lie groupoid $G_1 \rightrightarrows ...