The aim of this paper is to construct a natural mapping ${\check{C}}_k$, $k=1,2,3,\cdots$, from the multiplicative $K$-theory $K\left(X\right)$ of a differential manifold $X$, associated to the trivial filtration of the de Rham complex, as defined by M. Karoubi in [C. R. Acad. Sci., Paris, Sér. I 302, 321-324 (1986; Zbl 0593.55004)] to the odd cohomology $H_s^{2k-1}(X;C^{*})$. By using this mapping, the author associates to any flat complex vector bundle $E$ on $X$ characteristic classes ${\check{C}}_k\left(E\right)\in H_{dR}^{2k-1}(X;C^{*})$ analogous to the classes studied by S. Chern, J. Cheeger and 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)].

EUDML-ID : urn:eudml:doc:220807
Mots clés:

@article{701504,
     title = {A K-theoretic approach to Chern-Cheeger-Simons invariants},
     booktitle = {Proceedings of the Winter School "Geometry and Physics"},
     series = {GDML\_Books},
     publisher = {Circolo Matematico di Palermo},
     address = {Palermo},
     year = {1993},
     pages = {[27]-34},
     mrnumber = {MR1246617},
     zbl = {0790.57015},
     url = {http://dml.mathdoc.fr/item/701504}
}

Pekonen, Osmo. A K-theoretic approach to Chern-Cheeger-Simons invariants, dans Proceedings of the Winter School "Geometry and Physics", GDML_Books,  (1993), pp. [27]-34. http://gdmltest.u-ga.fr/item/701504/