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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

Cohomology for the ergodic actions of countable groups


Author: Joel J. Westman
Journal: Proc. Amer. Math. Soc. 30 (1971), 318-320
MSC: Primary 28.70; Secondary 18.00
MathSciNet review: 0280683
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Abstract: Certain aspects of Mackey's theory of virtual groups were fitted into a cohomology theory for ergodic groupoids in a previous paper by the author. Here we relate the groupoid cohomology for ergodic groupoids that arise (by Mackey's construction) from ergodic actions of countable groups to the usual group cohomology. In case the countable group is a free group, we find that the groupoid cohomology in dimension $ > 1$ is $ = \{ 0\} $.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1971-0280683-1
PII: S 0002-9939(1971)0280683-1
Keywords: Ergodic groupoid, virtual group, ergodic action, cohomology, countable group
Article copyright: © Copyright 1971 American Mathematical Society