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# Global quotients among toric Deligne-Mumford stacks

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### Abstract

This work characterizes global quotient stacks---smooth stacks associated to a finite group acting a manifold---among smooth quotient stacks $$[M/G]$$, where $$M$$ is a smooth manifold equipped with a smooth proper action by a Lie group $$G$$. The characterization is described in terms of the action of the connected component $$G_0$$ on $$M$$ and is related to (stacky) fundamental group and covering theory. This characterization is then applied to smooth toric Deligne-Mumford stacks, and global quotients among toric DM stacks are then characterized in terms of their associated combinatorial data of stacky fans.

### Most cited references8

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### ON A GENERALIZATION OF THE NOTION OF MANIFOLD

(1956)
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### Twisted Orbifold K-Theory

(2001)
We use equivariant methods to establish basic properties of orbifold K-theory. We introduce the notion of twisted orbifold K-theory in the presence of discrete torsion, and show how it can be explicitly computed for global quotients.
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### Orbifold cohomology for global quotients

(2003)
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### Author and article information

###### Journal
2013-02-02
1302.0385