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On the Farrell-Jones conjecture for higher algebraic $K$-theory

Author(s): Arthur Bartels; Holger Reich
Journal: J. Amer. Math. Soc. 18 (2005), 501-545.
MSC (2000): Primary 19D50; Secondary 53C12
Posted: March 30, 2005
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Abstract: We prove the Farrell-Jones Conjecture for the algebraic $K$-theory of a group ring $R \Gamma$ in the case where the group $\Gamma$ is the fundamental group of a closed Riemannian manifold with strictly negative sectional curvature. The coefficient ring $R$ is an arbitrary associative ring with unit and the result applies to all dimensions.

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Additional Information:

Arthur Bartels
Affiliation: Fachbereich Mathematik, Universität Münster, Einsteinstr. 62, 48149 Münster, Germany
Email: bartelsa@math.uni-muenster.de

Holger Reich
Affiliation: Fachbereich Mathematik, Universität Münster, Einsteinstr. 62, 48149 Münster, Germany
Email: reichh@math.uni-muenster.de

DOI: 10.1090/S0894-0347-05-00482-0
PII: S 0894-0347(05)00482-0
Keywords: $K$-theory, group rings, controlled algebra
Received by editor(s): August 5, 2003
Posted: March 30, 2005
Copyright of article: Copyright 2005, American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.

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