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Topological structure of translation-invariant noncommutative Yang-Millstheories are studied by means of a cohomology theory, so calledstar-cohomology, which plays an intermediate role between de Rham and cyclic(co)homology theory for noncommutative algebras and gives rise to acohomological formulation comparable to Seiberg-Witten map.

star-Cohomology, Connes-Chern Characters, and Anomalies in General Translation-Invariant Noncommutative Yang-Mills