# Tagged Questions

**8**

votes

**1**answer

151 views

### Construction of the Lie functor: left vs. right invariant vector fields on Lie groups and Lie groupoids

When constructing the Lie algebra $L(G)$ of a Lie group $G$, one usually uses the identification of the tangent space $T_1 G$ with left invariant vector fields $\mathcal{V}^l(G)$ to construct the Lie ...

**6**

votes

**1**answer

98 views

### Integrating representations of Lie algebroids

If $A \to M$ is a Lie algebroid over a smooth manifold $M$ then a representation of $A$ is a vector bundle $E \to M$ with a flat $A$-connection
$$
\nabla : \Gamma(E) \to \Gamma(E\otimes A^*).
$$
If ...

**4**

votes

**0**answers

81 views

### Is this groupoid a model for the derived fixed-point locus of the free loop space?

In this paper, John Baez and Urs Schreiber define (see Definition 2.16) a Lie groupoid (there called a '2-space') associated to any manifold $M$. In fact it is a bundle of Lie groups over $M$ thought ...

**2**

votes

**2**answers

291 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 ...

**5**

votes

**2**answers

471 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 - ...

**4**

votes

**2**answers

465 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

396 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**

votes

**2**answers

811 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 ...