# Tagged Questions

**19**

votes

**3**answers

813 views

### What tools cannot work for orbifolds?

Consider all of your basic constructions/tools/theorems for manifolds: fundamental group, Euler characteristic, triangulations, orientation, smoothness, bundle structure, cobordisms, etc.. Viewing ...

**4**

votes

**2**answers

316 views

### How to specify a finite group up to inner automorphism?

I want some finite set of data to which I can canoically associate a "group up to inner automorphism", and which can be constructed canoically from a "group up to inner automorphism". I have a few ...

**21**

votes

**2**answers

707 views

### Cobordism of orbifolds?

Is it possible to setup classical cobordism theory in the context of orbifolds? For example, let's consider the free abelian group generated by oriented smooth orbifolds and quotient by those which ...

**13**

votes

**1**answer

686 views

### Homotopy theory of topological stacks/orbifolds

Motivation $\newcommand{\T}{\mathscr{T}}$
I have many times found myself saying some variant of the following. Let $\T_g$ be the Teichmüller space of a surface of genus $g$, and $\Gamma_g$ its ...

**8**

votes

**1**answer

317 views

### tangent bundles of orbifolds

Hello,
I want to take a unit $n$-ball $B_n$ and quotient it by some subgroup $G \subset \mathbb{Z}_2^n$.
Here is a sketch of the construction: take the obvious inscribed $n$-hypercube of $B_n$; we ...

**6**

votes

**1**answer

390 views

### Stable homotopy theory of orbifolds

Is there a notion of stable homotopy, spectrum, or a stable homotopy category which corresponds to orbifolds and orbispaces, in the same way that classical stable homotopy theory corresponds to ...

**3**

votes

**1**answer

528 views

### A simple minded Poincare duality for orbifolds?

Suppose $X^n$ is an orientable compact orbifold (without boundary) with stabilisers in codimesnion 2, and $\bar X^n$ is the underlying topological space. We can assume moreover that $X^n$ is a ...

**8**

votes

**7**answers

1k views

### Orbifold fundamental group in terms of loops?

In chapter 13 in his notes on 3-manifolds, Thurston defines the orbifold fundamental group to be the group of deck transformations of the universal cover of the orbifold. He also makes a statement ...

**2**

votes

**2**answers

400 views

### Branched coverings over orbifolds with reflector lines

It is well known that if $F\to B$ is a $n$-finite branched covering over an orbifold with cone-points then the orbifold Euler's characteristics are related via ...