All Questions
Tagged with orbifolds differential-topology
10 questions
8
votes
1
answer
429
views
Gluing of orbifolds
Suppose that $P$ and $Q$ are $n$-dimensional orbifolds, with boundaries. Suppose also that there is an isomorphism $f \colon \partial P \rightarrow \partial Q$ (as orbifolds). Is there a way to glue $...
- 781
8
votes
0
answers
178
views
Smooth sub-orbifolds in the language of stacks
In most geometric categories, "monomorphism" is too general to describe useful notions of "embedding". This is the case e.g. for schemes, complex manifolds, and differentiable manifolds.
So "embedding"...
- 23.3k
2
votes
0
answers
137
views
Does any smooth oriented closed orbifold have a fundamental class
This thread:triangulation of orbifolds
has shown that any smooth closed orbifold has a triangulation. My further question is: if the difference of any two triangulations $P$ and $Q$ is a boundary of a ...
- 781
7
votes
0
answers
484
views
manifold branched covering space for orbifolds
An orbifold structure on some topological space $X$ is a covering of $X$ with local quotient charts $V/G$, where $V$ is some connected manifold and $G$ effectively acts on $V$ via a finite group of ...
2
votes
2
answers
261
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 $T^{2}/Z_{k}\times Z_{k}$ ...
- 405
1
vote
0
answers
94
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 R^{1,4m-3}...
- 371
10
votes
2
answers
3k
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 ...
- 515
1
vote
1
answer
208
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 ...
- 15.5k
6
votes
1
answer
503
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 ...
6
votes
3
answers
485
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 $\gamma_x$...
- 33.3k