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Translation Groupoids and Orbifold Cohomology

  Published:2009-12-04
 Printed: Jun 2010
  • Dorette Pronk
  • Laura Scull
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Abstract

We show that the bicategory of (representable) orbifolds and good maps is equivalent to the bicategory of orbifold translation groupoids and generalized equivariant maps, giving a mechanism for transferring results from equivariant homotopy theory to the orbifold category. As an application, we use this result to define orbifold versions of a couple of equivariant cohomology theories: K-theory and Bredon cohomology for certain coefficient diagrams.
Keywords: orbifolds, equivariant homotopy theory, translation groupoids, bicategories of fractions orbifolds, equivariant homotopy theory, translation groupoids, bicategories of fractions
MSC Classifications: 57S15, 55N91, 19L47, 18D05, 18D35 show english descriptions Compact Lie groups of differentiable transformations
Equivariant homology and cohomology [See also 19L47]
Equivariant $K$-theory [See also 55N91, 55P91, 55Q91, 55R91, 55S91]
Double categories, $2$-categories, bicategories and generalizations
Structured objects in a category (group objects, etc.)
57S15 - Compact Lie groups of differentiable transformations
55N91 - Equivariant homology and cohomology [See also 19L47]
19L47 - Equivariant $K$-theory [See also 55N91, 55P91, 55Q91, 55R91, 55S91]
18D05 - Double categories, $2$-categories, bicategories and generalizations
18D35 - Structured objects in a category (group objects, etc.)
 

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