Graded Brauer groups and $K$-theory with local coefficients

Peter Donavan; Max Karoubi

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Characteristic classes for $A$ -bundles

Cap, Andreas, Schichl, Hermann

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The authors generalize a construction of Connes by defining for an $A$ -bundle $E$ over smooth manifold $X$ and a reduced cyclic cohomology class $c$ a sequence of de Rham cohomology classes $c h_{c}^{k} (E)$ . Here $A$ is a convenient algebra, defined by the authors, and $E$ is a locally trivial bundle with standard fibre a right finitely generated projective $A$ -module and bounded $A$ -modules homomorphisms as transition functions.