K-theory, flat bundles and the Borel classes

Bjørn Jahren

Fundamenta Mathematicae (1999)

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

Abstract

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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.

How to cite

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Jahren, 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

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