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Higher cohomology for Abelian groups of toral automorphisms

Published online by Cambridge University Press:  19 September 2008

Anatole Katok  and
Svetlana Katok
Anatole Katok
Affiliation:
Department of Mathematics, The Pennsylvania State University, University Park, PA 16802, USA (e-mail: [email protected])
Svetlana Katok
Affiliation:
Department of Mathematics, The Pennsylvania State University, University Park, PA 16802, USA (e-mail: [email protected])
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Abstract

We give a complete description of smooth untwisted cohomology with coefficients in ℝl for ℤk-actions by hyperbolic automorphisms of a torus. For 1 ≤ n ≤ k − 1 the nth cohomology trivializes, i.e. every cocycle is cohomologous to a constant cocycle via a smooth coboundary. For n = k a counterpart of the classical Livshitz Theorem holds: the cohomology class of a smooth k-cocycle is determined by periodic data.

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 15 , Issue 3 , June 1995 , pp. 569 - 592
Copyright
Copyright © Cambridge University Press 1995

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