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Characteristic classes for $A$-bundles

Andreas Čap, Hermann Schichl

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Abstract

Abstract. We consider locally trivial bundles over smooth manifolds, whose fibers are finitely generated projective modules over a convenient algebra A. For such a bundle E → X and a bounded reduced cyclic cocycle c on A we construct a sequence chk c (E) of de–Rham cohomology classes on X, which are an analog of the classical Chern character. We show that these classes depend only on the cohomology class of c and behave natural under various constructions. 1.

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Abstract. We consider locally trivial bundles over smooth manifolds, whose fibers are finitely generated projective modules over a convenient algebra A. For such a bundle E → X and a bounded reduced cyclic cocycle c on A we construct a sequence chk c (E) of de–Rham cohomology classes on X, which are an analog of the classical Chern character. We show that these classes depend only on the cohomology class of c and behave natural under various constructions. 1.

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Available abstract

Abstract. We consider locally trivial bundles over smooth manifolds, whose fibers are finitely generated projective modules over a convenient algebra A. For such a bundle E → X and a bounded reduced cyclic cocycle c on A we construct a sequence chk c (E) of de–Rham cohomology classes on X, which are an analog of the classical Chern character. We show that these classes depend only on the cohomology class of c and behave natural under various constructions. 1.

Key concepts: Chern–Weil homomorphism, Mathematics, Pure mathematics, Characteristic class, Vector bundle, Chern class, De Rham cohomology, Cohomology

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