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

Pekonen, Osmo. "A K-theoretic approach to Chern-Cheeger-Simons invariants." Proceedings of the Winter School "Geometry and Physics". Palermo: Circolo Matematico di Palermo, 1993. [27]-34. <http://eudml.org/doc/220807>.

@inProceedings{Pekonen1993,
abstract = {The aim of this paper is to construct a natural mapping $\check\{C\}_k$, $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 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 $\check\{C\}_k(E) \in H_\{dR\}^\{2k-1\} (X;C^*)$ 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)].},
author = {Pekonen, Osmo},
booktitle = {Proceedings of the Winter School "Geometry and Physics"},
keywords = {Proceedings; Geometry; Srní (Czechoslovakia); Physics},
location = {Palermo},
pages = {[27]-34},
publisher = {Circolo Matematico di Palermo},
title = {A K-theoretic approach to Chern-Cheeger-Simons invariants},
url = {http://eudml.org/doc/220807},
year = {1993},
}

TY - CLSWK
AU - Pekonen, Osmo
TI - A K-theoretic approach to Chern-Cheeger-Simons invariants
T2 - Proceedings of the Winter School "Geometry and Physics"
PY - 1993
CY - Palermo
PB - Circolo Matematico di Palermo
SP - [27]
EP - 34
AB - The aim of this paper is to construct a natural mapping $\check{C}_k$, $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 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 $\check{C}_k(E) \in H_{dR}^{2k-1} (X;C^*)$ 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)].
KW - Proceedings; Geometry; Srní (Czechoslovakia); Physics
UR - http://eudml.org/doc/220807
ER -