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Title: A K-theoretic approach to Chern-Cheeger-Simons invariants (English)
Author: Pekonen, Osmo
Language: English
Journal: Proceedings of the Winter School "Geometry and Physics"
Issue: 1991
Pages: [27]-34
Category: math
Summary: The aim of this paper is to construct a natural mapping $\check C\sb k$, $k=1,2,3,\dots$, 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 {\it M. Karoubi} in [C. R. Acad. Sci., Paris, S\'er. I 302, 321-324 (1986; Zbl 0593.55004)] to the odd cohomology $H\sb s\sp{2k-1} (X;C\sp*)$. By using this mapping, the author associates to any flat complex vector bundle $E$ on $X$ characteristic classes $\check C\sb k(E) \in H\sb{dR}\sp{2k-1} (X;C\sp*)$ analogous to the classes studied by {\it S. Chern}, {\it J. Cheeger} and {\it J. Simons} in [Differential characters and geometric invariants, in `Geometry and topology', Lect. Notes Math. 1167, 50-80 (1985; Zbl 0621.57010), Characteristic forms and geometric invariants, Ann. Math., II. Ser. 99, 48-69 (1974; Zbl 0283.53036)]. (English)
MSC: 19L10
MSC: 55N15
MSC: 57R19
MSC: 57R20
MSC: 58G10
MSC: 58J20
idZBL: Zbl 0790.57015
idMR: MR1246617
Date available: 2009-07-13T21:28:39Z
Last updated: 2012-09-18
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