Classifying spaces and Bredon (co)homology for transitive groupoids
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- by Carla Farsi, Laura Scull and Jordan Watts PDF
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Abstract:
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.References
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Additional Information
- Carla Farsi
- Affiliation: Department of Mathematics, University of Colorado at Boulder, Boulder, Colorado 80309-0395
- MR Author ID: 311031
- Email: carla.farsi@colorado.edu
- Laura Scull
- Affiliation: Department of Mathematics, Fort Lewis College, Durango, Colorado 81301
- MR Author ID: 684707
- Email: scull_l@fortlewis.edu
- Jordan Watts
- Affiliation: Department of Mathematics, Central Michigan University, Mt. Pleasant, Michigan 48859
- MR Author ID: 901837
- Email: jordan.watts@cmich.edu
- Received by editor(s): September 1, 2018
- Received by editor(s) in revised form: May 30, 2019, October 17, 2019, and November 4, 2019
- Published electronically: February 26, 2020
- Additional Notes: The first author was partially supported by the Simons Foundation grant #523991.
- Communicated by: Mark Behrens
- © Copyright 2020 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 148 (2020), 2717-2737
- MSC (2010): Primary 22A22, 55N91; Secondary 55R91
- DOI: https://doi.org/10.1090/proc/14930
- MathSciNet review: 4080910