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A K-theoretic approach to Chern-Cheeger-Simons invariants

Pekonen, Osmo — 1993

Proceedings of the Winter School "Geometry and Physics"

The aim of this paper is to construct a natural mapping C ˇ k , k = 1 , 2 , 3 , , from the multiplicative K -theory K ( X ) of a differential manifold X , associated to the trivial filtration of the de Rham complex, as defined by in [C. R. Acad. Sci., Paris, Sér. I 302, 321-324 (1986; Zbl 0593.55004)] to the odd cohomology H s 2 k - 1 ( X ; C * ) . By using this mapping, the author associates to any flat complex vector bundle E on X characteristic classes C ˇ k ( E ) H d R 2 k - 1 ( X ; C * ) analogous to the classes studied by , and in [Differential characters and geometric invariants,...

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