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Instances of cohomological triviality and rigidity

Published online by Cambridge University Press:  19 September 2008

William Parry
William Parry
Affiliation:
Department of Mathematics, University of Warwick, Coventry CV4 7AL, UK
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Abstract

We consider a compact metric zero-dimensional abelian group X and mixing ℤ2 (or ℤ2+) actions by automorphisms (or endomorphisms). We provide various instances of cohomological triviality and rigidity for cocycles taking values in finite groups.

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 15 , Issue 4 , August 1995 , pp. 685 - 696
Copyright
Copyright © Cambridge University Press 1995

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References

REFERENCES

[1]Katok, A. and Schmidt, K.. The cohomology of expansive ℤd actions by automorphisms of compact abelian groups. (Preprint.)Google Scholar
[2]Kitchens, B. and Schmidt, K.. Automorphisms of compact groups. Ergod. Th. & Dynam. Sys. 9 (1989), 691–735.CrossRefGoogle Scholar
[3]Kitchens, B. and Schmidt, K.. Markov subgroups of . Contemp. Math. 135 (1992), 265–683.CrossRefGoogle Scholar
[4]Ledrappier, F.. Un champ markovien peutetre d'entropie n ulle et mélangeant. C. R. Acad. Sci. Paris Ser. A. 287 (1978), 561–562.Google Scholar
[5]Livsic, A.. Cohomology of dynamical systems. Math. U.S.S.R. Izv. 6 (1972), 1278–1301.CrossRefGoogle Scholar
[6]Rudolph, D.. ×2 and ×3 invariant measures and entropy. Dynam. Sys. 10 (1990), 395–406.Google Scholar
[7]Schmidt, K.. Cohomological rigidity of algebraic ℤd-actions. To appear.Google Scholar