Cohomology for the ergodic actions of countable groups
HTML articles powered by AMS MathViewer
- by Joel J. Westman PDF
- Proc. Amer. Math. Soc. 30 (1971), 318-320 Request permission
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 $= \{ 0\}$.References
- Serge Lang, Rapport sur la cohomologie des groupes, W. A. Benjamin, Inc., New York-Amsterdam, 1967 (French). MR 0212073
- George W. Mackey, Ergodic theory and virtual groups, Math. Ann. 166 (1966), 187–207. MR 201562, DOI 10.1007/BF01361167 S. Mac Lane, Homology, Die Grundlehren der math. Wissenschaften, Band 114, Academic Press, New York; Springer-Verlag, Berlin, 1963. MR 28 #122.
- Joel J. Westman, Cohomology for ergodic groupoids, Trans. Amer. Math. Soc. 146 (1969), 465–471. MR 255771, DOI 10.1090/S0002-9947-1969-0255771-1
Additional Information
- © Copyright 1971 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 30 (1971), 318-320
- MSC: Primary 28.70; Secondary 18.00
- DOI: https://doi.org/10.1090/S0002-9939-1971-0280683-1
- MathSciNet review: 0280683