a1 Department of Mathematics, The Pennsylvania State University, University Park, PA 16802, USA (e-mail: firstname.lastname@example.org)
a2 Department of Mathematics, The Pennsylvania State University, University Park, PA 16802, USA (e-mail: email@example.com)
We give a complete description of smooth untwisted cohomology with coefficients inl 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.
(Received December 12 1993)
(Revised June 28 1994)
† The work of the authors was partially supported by NSF grants DMS-9017995 and DMS-9207728, respectively.