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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.

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          Most cited references 8

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          ON A GENERALIZATION OF THE NOTION OF MANIFOLD

           I Satake (1956)
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            Twisted Orbifold K-Theory

            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

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                Author and article information

                Journal
                2013-02-02
                1302.0385

                http://arxiv.org/licenses/nonexclusive-distrib/1.0/

                Custom metadata
                57R18, 53D20, 14M25, 14D23
                23 pages, 3 figues
                math.DG math.AG math.SG

                Geometry & Topology

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