00-58 Oliver Knill

On the cohomology of discrete abelian group actions (59K, LATeX 2e) Feb 2, 00

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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.

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