The Farrell-Jones Isomorphism Conjecture for finite covolume hyperbolic actions and the algebraic 𝐾-theory of Bianchi groups

Berkove, E.; Farrell, F.; Juan-Pineda, D.; Pearson, K.

doi:10.1090/S0002-9947-00-02529-0

The Farrell-Jones Isomorphism Conjecture for finite covolume hyperbolic actions and the algebraic $K$-theory of Bianchi groups
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by E. Berkove, F. T. Farrell, D. Juan-Pineda and K. Pearson PDF

Trans. Amer. Math. Soc. 352 (2000), 5689-5702 Request permission

Abstract:

We prove the Farrell-Jones Isomorphism Conjecture for groups acting properly discontinuously via isometries on (real) hyperbolic $n$-space $\mathbb {H}^n$ with finite volume orbit space. We then apply this result to show that, for any Bianchi group $\Gamma$, $Wh(\Gamma )$, $\tilde K_0(\mathbb {Z}\Gamma )$, and $K_i(\mathbb {Z}\Gamma )$ vanish for $i\leq -1$.

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