2
votes
2answers
150 views

Topological invariants of toroidal orbifolds

Which are the most powerful topological invariants of toroidal orbifolds? In particular I am looking for topological invariants of two-dimensional toroidal orbifolds such as $T^{2}/Z_{k}\times Z_{k}$ ...
1
vote
0answers
74 views

Pseudo-Euclidean orbifolds

Are there any papers (reviews) devoted mainly to pseudo-Euclidean orbifolds in mathematics and physics (e.g. string theory)? A more specific question is related to orbifolds of type $\mathbb ...
7
votes
2answers
815 views

Euler characteristic of orbifolds

Hello, Suppose $M$ is a compact oriented smooth manifold and $G$ is a finite group acting on it. Then it is well-known, although I have yet to find a proof or derivation of it, that the (normal ...
1
vote
1answer
176 views

When do maps of ineffective orbifolds descend to their effective part?

If $$f:\mathscr{X} \to \mathscr{Y}$$ is a map between (possibly ineffective) orbifolds (in the sense of differentiable stacks, or orbifold groupoids), does it follow that $f$ induces a map between ...
5
votes
1answer
323 views

Diffeomorphism groups of orbifolds

A lot is known about geometric and topological properties of diffeomorphism groups of surfaces (here, I am mainly thinking about the work of Smale and Eells-Elworthy). Is there anything known for ...
5
votes
3answers
289 views

Smoothness of frame bundle of (global) orbifolds [reference request]

Background Let $(M,g)$ be a riemannian manifold and let $G$ be a finite group acting effectively and isometrically on $M$. Recall that this means that for all $x \in G$, the diffeomorphism ...