Questions tagged [orbifolds]
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12 questions from the last 365 days
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Questions about classifying hyperkahler ALE orbifolds
Kronheimer classified all smooth hyperkahler ALE 4-manifolds. In his paper, he constructed, unsing hyperkahler qutient, a complete family of hyperkahler ALEs for each finite group $\Gamma<\mathrm{...
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Audin's claim on Seifert manifolds, and generalization to orbifolds
In Audin's book on symplectic torus actions, she states the following proposition:
Proposition I.3.8: Let $W$ be an oriented Seifert manifold. Let $n$ be a common multiple of the orders of the ...
- 226
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Signature vs commensurability
If a closed oriented $4n$-dimensional manifold $M$ has an orientation-reversing homeomorphism, then the signature $\sigma(M)$ of the intersection form vanishes. More generally, $\sigma(M) = 0$ if $M$ ...
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Suppose that $G$ is a finite subgroup of ${\rm SO}(3)$. Is there a *smooth* self-map of ${\bf R}^3$ whose fibers are precisely the orbits of $G$?
$\newcommand\R{\mathbf R}\DeclareMathOperator\SO{SO}\newcommand\C{\mathbf C}$The question is motivated by the theory of orbifolds. If $\mathcal O$ is an orientable $3$-orbifold (without boundary), an ...
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Is there a generalization of the Diameter Sphere Theorem to orbifolds?
The Diameter Sphere Theorem of Grove and Shiohama asserts that if $M$ is a compact Riemannian manifold with sectional curvature bounded from bellow by 1 and diameter greater than $\pi/2$, then $M$ is ...
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Moduli space of complex and anti-complex tori?
$\DeclareMathOperator\GL{GL}\DeclareMathOperator\SO{SO}\DeclareMathOperator\SL{SL}$By Will Sawin's answer to Moduli Spaces of Higher Dimensional Complex Tori the moduli space of complex $d$-tori is $X ...
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Quotient of GL(N) by row permutations
Let $\mathcal{M}$ be the quotient space of $GL(n)$ over $\mathbb{R}$ under the action of the permutation group $S^n$ acting as follows
$$
X\sim Y \Leftrightarrow (\exists \pi \in S^n)\, X_i = Y_{\pi(i)...
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Complex of groups of an orbifold
I have just started to look a bit into orbifolds. The English Wikipedia page mentions that there is a complex of groups associated to an (effective) orbifold.
However I couldn't manage to find the ...
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Good orbifold and Ricci flow with Dirichlet boundary conditions on $\Sigma$
An orbifold $\mathcal O$ is a metrizable topological space equipped with an atlas modeled on $\Bbb R^n/\Gamma, \Gamma<O(n)$ finite. Let $\Sigma$ be the singular locus i.e. points modeled on $\...
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References for orbifold curves
I am looking for a good reference (if there is any) for the theory of orbifold curves from the perspective of stacks. By an orbifold curve I mean something like a $1$-dimensional irreducible Deligne-...
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How to prove the gluing-condition for a pseudogroup induced by an étale Lie groupoid?
Let $G_1\substack{\to \\ \to}G_0$ be an étale Lie groupoid, whose source- and target-maps are denoted by $s$ and $t$, respectively. Let
\begin{equation}
\Psi=\{(t|_U)\circ(s|_U)^{-1}:\text{$U$ is ...
- 131
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Non compact Seifert manifolds
A Seifert manifold $M$ is a $3$-dimensional orientable smooth manifold with an effective circle action with no fixed points.
Closed connected Seifert manifolds are classified up to an equivariant ...
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