# Questions tagged [lie-groupoids]

The tag has no usage guidance.

55 questions
Filter by
Sorted by
Tagged with
110 views

### Notions of Lie 2-groupoids

The term Lie $2$-groupoid is used in the literature in more than one context. Some examples are given below: Ginot and Stiénon's paper $G$-gerbes, principal $2$-group bundles and characteristic ...
52 views

### Models for computing cohomology of Lie groupoids

Given a Lie groupoid $\mathcal{G}=[\mathcal{G}_1\rightrightarrows \mathcal{G}_0]$, let $\mathcal{G}_\bullet$ be the associated simplicial manifold. Let $\Omega^\bullet(\mathcal{G}_\bullet)$ be the ...
135 views

### What are the Newton groupoids from Drinfeld's paper on the Grinberg-Kazhdan theorem?

The paper the Grinberg-Kazhdan formal arc theorem and the Newton groupoids by Drinfeld seems to contain many interesting things which are beyond me. For now, I am trying to get some intuition for the ...
265 views

### Why the third stage of Cech nerve a Lie 2-groupoid?

In the page https://ncatlab.org/nlab/show/Lie+2-groupoid the Lie 2-groupoid is defined as the 2 truncated $\infty$-Lie groupoid. I am not much comfortable with the language of higher category theory ...
47 views

### Reference request : Quotient manifold theorem for Lie groupoid action on a manifold

Let $G$ be a Lie group and $M$ be a smooth manifold. Let $G\times M\rightarrow M$ be a smooth map giving a free, proper action of $G$ On $M$. Then, by quotient manifold theorem, we see that there ...
54 views

### Lie group (topological group) action on differentiable stack (topological stack)

Let $G$ be a Lie group and $\mathcal{D}$ be a differentiable stack (I am also ok to start with a topological group and topological stack). I have seen someone mentioning somewhere that the notion of ...
116 views

### Lie groupoids being homotopy equivalent

Let $M,N$be two smooth manifolds. Let $f,g:M\rightarrow N$ be two smooth maps. We have the notion of a homotopy (smooth homotopy) from the maps $f$ to the map $g$. Is there a similar concept for ...
285 views

254 views

### Automorphisms of which structure form a Lie groupoid

Given a manifold $M$, the collection of all automorphisms of $M$, denoted by $\text{Aut}(M)$ forms a Lie group. Do we have similar setting in case of Lie groupoid? Is there "a structure" whose "...
141 views

### Isotropy subgroupoid of a regular Lie groupoid

Let $(G\rightrightarrows M)$ be a Lie groupoid (i.e. a groupoid with source map $s$ and target map $t$ such that $G,M$ are smooth manifolds and the structural maps are all smooth (and $s$,$t$ are ...
127 views

### Condition on a Lie groupoid to be represented by manifold/group or an action groupoid

Let $\mathcal{G}$ be a Lie groupoid. I am thinking of following questions. When do we know $\mathcal{G}$ is weakly/Morita equivalent to a Lie groupoid of the form $(G\rightrightarrows *)$ for some ...
283 views

210 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 ...
235 views

590 views

### Why study orbifolds? [closed]

Question is as in the title. Why study orbifolds? I study orbifolds as locally compact Hausdorff spaces $X$ having an orbifold structure, i.e., there exists an orbifold groupoid (proper foliatio. ...
218 views

### Necessity/Motivation for generalised homomorpisms

I am reading Ieke Moerdijk's article "Orbifolds as Groupoids : an Introduction". In that notes author defines a notion of generalized map between Lie groupoids. Let $\mathcal{G}$ and $\mathcal{H}$...
241 views

### Isotropy group of a Lie groupoid is a Lie group

I am trying to see that Isotropy group/object group/vertex group of a Lie groupoid is a Lie group. Let $\mathcal{G}$ be a Lie groupoid and $x$ be an object in $\mathcal{G}$ i.e., $x\in \mathcal{G}_0$...
383 views

366 views

### What are the possible symplectic structures on a given Lie groupoid?

Recall the definition of a symplectic groupoid. Roughly this is a Lie groupoid such that the object manifold is Poisson, and the arrow manifold is symplectic such that the symplectic form is ...
698 views

### Internal equivalence implies weak equivalence for Frechet Lie groupoids?

It is a known theorem that an internal equivalence of Lie groupoids (finite dimensional manifolds!) - that is an equivalence in the 2-category of Lie groupoids, smooth functors and transformations - ...
232 views

### Which makes Lie groupoids so nice?

This is a continuation of my previous question. A) Morphisms in (1') are basically internal anafunctors, their compositions heavily use (and only) pullback/limit. B) Bibundles in (2) are basically ...