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

Bartels, Arthur; Reich, Holger

doi:10.1090/S0894-0347-05-00482-0

On the Farrell-Jones conjecture for higher algebraic $K$-theory
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by Arthur Bartels and Holger Reich

J. Amer. Math. Soc. 18 (2005), 501-545

DOI: https://doi.org/10.1090/S0894-0347-05-00482-0

Published electronically: 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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