Non-abelian cohomology of abelian Anosov actions

Anatole Katok, Viorel Niţicǎ, Andrei Török

Research output: Contribution to journalArticle

20 Scopus citations

Abstract

We develop a new technique for calculating the first cohomology of certain classes of actions of higher-rank abelian groups (ℤk and ℝk, k ≥ 2) with values in a linear Lie group. In this paper we consider the discrete-time case. Our results apply to cocycles of different regularity, from Hölder to smooth and real-analytic. The main conclusion is that the corresponding cohomology trivializes, i.e. that any cocycle from a given class is cohomologous to a constant cocycle. The principal novel feature of our method is its geometric character; no global information about the action based on harmonic analysis is used. The method can be developed to apply to cocycles with values in certain infinite dimensional groups and to rigidity problems.

Original languageEnglish (US)
Pages (from-to)259-288
Number of pages30
JournalErgodic Theory and Dynamical Systems
Volume20
Issue number1
DOIs
StatePublished - Feb 2000

All Science Journal Classification (ASJC) codes

  • Mathematics(all)
  • Applied Mathematics

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