Questions tagged [orbifolds]
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What is meant by smooth orbifold?
There seems to be some confusion over what the tangent space to a singular point of an orbifold is.
On the one hand there is the obvious notion that smooth structures on orbifolds lift to smooth $G$-...
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Proper and etale groupoid is locally a translation groupoid
I am reading Orbifolds as Groupoids: an Introduction by Ieke Moerdijk.
In page $8$ when explaining local charts, it says the following :
Let $\mathcal{G}$ be a Lie groupoid. For an open set $U\...
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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 "...
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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 ...
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Conditions for underlying space of an orbifold $\Bbb T^n/\Gamma$ to be a sphere?
Given a $n$-dimensional torus, is it always possible to find a discrete action to produce an orbifold such that its underlying space is the $n$-dimensional sphere? Or does it only happens for specific ...
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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 ...
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How should one understand orbifold fundamental groups?
I am studying orbifold fundamental group (or more generally orbifold homotopy groups). In a nutshell, my questions is: what are they intuitively? In what follows I give definitions and more precise ...
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Is every rational realized as the Euler characteristic of some manifold or orbifold?
Let me first ask the question for two-dimensional compact, connected manifolds and orbifolds.
Then, if the answer is No, one can remove various conditions on the dimension,
and allow non-compact ...
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What is an example of an orbifold which is not a topological manifold?
In Thurston's book The Geometry and Topology of Three-Manifolds it is proven that the underlying space of a two-dimensional orbifold is always a topological surface.
Are there any easy examples of ...
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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 ...
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Duality between orbifold and quasi-Hopf algebra (twisted quantum doubles)
A quick Question:
Is there some duality known between the quasi Hopf algebra
$D^\omega(H)$ of a finite group $H$ to an orbifold model (such as
SU(2)/$G$ or SO(3)/$G$ orbifold of some group $G$)? What ...
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Is the Čech cohomology of an orbifold isomorphic to its singular cohomology?
Let $\mathcal{O}$ be a finite-dimensional, paracompact, Hausdorff, smooth (and compact, if it helps) orbifold. Is there an isomorphism between the real Čech cohomology and singular cohomology of the ...
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Is there a topological Chevalley-Shephard-Todd Theorem?
Is the following true:
For a representation of a finite group $G$ on $\mathbb{C}^n$, the quotient $\mathbb{C}^n/G$ is a topological manifold if and only if $G$ is generated by pseudo-reflections.
( ...
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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 ...
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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 $\mathcal{H}$...