Higher cohomology for Abelian groups of toral automorphisms

Anatoly Katok, Svetlana Katok

Research output: Contribution to journalArticlepeer-review

20 Scopus citations


We give a complete description of smooth untwisted cohomology with coefficients in l for k-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.

Original languageEnglish (US)
Pages (from-to)569-592
Number of pages24
JournalErgodic Theory and Dynamical Systems
Issue number3
StatePublished - Jan 1 1995

All Science Journal Classification (ASJC) codes

  • General Mathematics
  • Applied Mathematics


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