# K-theory, flat bundles and the Borel classes

Fundamenta Mathematicae (1999)

- Volume: 161, Issue: 1-2, page 137-153
- ISSN: 0016-2736

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topJahren, Bjørn. "K-theory, flat bundles and the Borel classes." Fundamenta Mathematicae 161.1-2 (1999): 137-153. <http://eudml.org/doc/212396>.

@article{Jahren1999,

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.},

author = {Jahren, Bjørn},

journal = {Fundamenta Mathematicae},

keywords = {algebraic -theory of integers; characteristic classes; flat bundles; Borel classes},

language = {eng},

number = {1-2},

pages = {137-153},

title = {K-theory, flat bundles and the Borel classes},

url = {http://eudml.org/doc/212396},

volume = {161},

year = {1999},

}

TY - JOUR

AU - Jahren, Bjørn

TI - K-theory, flat bundles and the Borel classes

JO - Fundamenta Mathematicae

PY - 1999

VL - 161

IS - 1-2

SP - 137

EP - 153

AB - 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.

LA - eng

KW - algebraic -theory of integers; characteristic classes; flat bundles; Borel classes

UR - http://eudml.org/doc/212396

ER -

## References

top- [1] A. J. Berrick, Characterization of plus-constructive fibrations, Adv. Math. 48 (1983), 172-176. Zbl0531.55012
- [2] A. Borel, Stable real cohomology of arithmetic groups, Ann. Sci. École Norm. Sup. (4) 7 (1974), 235-272. Zbl0316.57026
- [3] A. Borel, Cohomologie de $S{L}_{n}$ et valeurs de fonctions zêta aux points entiers, Ann. Scuola Norm. Sup. Pisa 4 (1977), 613-636. Zbl0382.57027
- [4] 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.
- [5] 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.
- [6] B. Jahren, On the rational K-theory of group rings of finite groups, preprint, Oslo, 1993.
- [7] J. D. S. Jones and B. W. Westbury, Algebraic K-theory, homology spheres, and the η-invariant, Warwick preprint 4/1993.
- [8] F. W. Kamber and Ph. Tondeur, Foliated Bundles and Characteristic Classes, Lecture Notes in Math. 493, Springer, 1975.
- [9] M. Karoubi, Homologie cyclique et K-théorie, Astérisque 149 (1987).
- [10] M. A. Kervaire, Smooth homology spheres and their fundamental groups, Trans. Amer. Math. Soc. 144 (1969), 67-72. Zbl0187.20401
- [11] 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. Zbl0284.12005

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