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Translation Groupoids and Orbifold Cohomology

Published online by Cambridge University Press:  20 November 2018

Dorette Pronk  and
Laura Scull
Dorette Pronk
Affiliation:
Department of Mathematics and Statistics, Dalhousie University, Halifax, NS, B3H 3J5, e-mail: pronk@mathstat.dal.ca
Laura Scull
Affiliation:
Department of Mathematics, Fort Lewis College, Durango, CO 81301-3999, USA, e-mail: scull l@fortlewis.edu
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Abstract

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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

57S1555N9119L4718D0518D35orbifoldsequivariant homotopy theorytranslation groupoidsbicategories of fractions
Type
Research Article
Information
Canadian Journal of Mathematics , Volume 62 , Issue 3 , 01 June 2010 , pp. 614 - 645
Copyright
Copyright © Canadian Mathematical Society 2010

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