K-theory, flat bundles and the Borel classes

Bjørn Jahren

ArticleOriginal scientific text

Title

K-theory, flat bundles and the Borel classes

Authors ¹

Affiliations

Department of Mathematics, University of Oslo, P.O. Box 1053 Blindern, 0316 Oslo, Norway

Abstract

Using Hausmann and Vogel's homology sphere bundle interpretation of algebraic K-theory, we construct K-theory invariants by a theory of characteristic classes for flat bundles. It is shown that the Borel classes are detected this way, as well as the rational K-theory of integer group rings of finite groups.

A. J. Berrick, Characterization of plus-constructive fibrations, Adv. Math. 48 (1983), 172-176.
A. Borel, Stable real cohomology of arithmetic groups, Ann. Sci. École Norm. Sup. (4) 7 (1974), 235-272.
A. Borel, Cohomologie de $S L_{n}$ et valeurs de fonctions zêta aux points entiers, Ann. Scuola Norm. Sup. Pisa 4 (1977), 613-636.
J.-C. Hausmann, Homology sphere bordism and Quillen plus construction, in: Algebraic K-Theory (Evanston, 1976), Lecture Notes in Math. 551, Springer, 1976, 170-181.
J.-C. Hausmann and P. Vogel, The plus construction and lifting maps from manifolds, in: Proc. Sympos. Pure Math. 32, Amer. Math. Soc., 1978, 67-76.
B. Jahren, On the rational K-theory of group rings of finite groups, preprint, Oslo, 1993.
J. D. S. Jones and B. W. Westbury, Algebraic K-theory, homology spheres, and the η-invariant, Warwick preprint 4/1993.
F. W. Kamber and Ph. Tondeur, Foliated Bundles and Characteristic Classes, Lecture Notes in Math. 493, Springer, 1975.
M. Karoubi, Homologie cyclique et K-théorie, Astérisque 149 (1987).
M. A. Kervaire, Smooth homology spheres and their fundamental groups, Trans. Amer. Math. Soc. 144 (1969), 67-72.
S. Lichtenbaum, Values of zeta functions, étale cohomology, and algebraic K-theory, in: Algebraic K-Theory II, Lecture Notes in Math. 342, Springer, 1973, 489-501.

Title

K-theory, flat bundles and the Borel classes

Affiliations

Abstract

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