Abstract
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 language | English (US) |
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Pages (from-to) | 569-592 |
Number of pages | 24 |
Journal | Ergodic Theory and Dynamical Systems |
Volume | 15 |
Issue number | 3 |
DOIs | |
State | Published - Jan 1 1995 |
All Science Journal Classification (ASJC) codes
- General Mathematics
- Applied Mathematics