Oliver Knill
On the cohomology of discrete abelian group actions
(59K, LATeX 2e)

ABSTRACT.  Generalizing a result of Depauw, we prove that the
geometric cohomology groups for a Z^d action
are in any dimension isomorphic to the Feldman-Moore
cohomology groups rsp. the algebraic
group cohomology groups. This result holds in the smooth,
topological or measurable category and for general Polish
groups as coefficient groups.
The groups discussed here lead to algebraic invariants of
dynamical systems like tiling dynamical systems and play a
role in classes of higher dimensional discrete random
difference operators.