Classifying spaces and Bredon (co)homology for transitive groupoids

Carla Farsi, Laura Scull, Jordan Watts

Research output: Contribution to journalArticlepeer-review


We define the orbit category for transitive topological groupoids and their equivariant CW-complexes. By using these constructions we define equivariant Bredon homology and cohomology for actions of transitive topological groupoids. We show how these theories can be obtained by looking at the action of a single isotropy group on a fiber of the anchor map, extending equivariant results for compact group actions. We also show how this extension from a single isotropy group to the entire groupoid action can be applied to the structure of principal bundles and classifying spaces.

Original languageEnglish
Pages (from-to)2717-2737
Number of pages21
JournalProceedings of the American Mathematical Society
Issue number6
StatePublished - 2020


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