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

E. Berkove, F. T. Farrell, D. Juan-Pineda, K. Pearson
2000 Transactions of the American Mathematical Society  
We prove the Farrell-Jones Isomorphism Conjecture for groups acting properly discontinuously via isometries on (real) hyperbolic n-space H n with finite volume orbit space. We then apply this result to show that, for any Bianchi group Γ, W h(Γ),K 0 (ZΓ), and K i (ZΓ) vanish for i ≤ −1.
doi:10.1090/s0002-9947-00-02529-0 fatcat:ofuanyhfrzegniavpswfl256um