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 $i\leq -1$.References
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Additional Information
- E. Berkove
- Affiliation: Department of Mathematics, Lafayette College, Easton, Pennsylvania 18042-1781
- Email: berkovee@lafayette.edu
- F. T. Farrell
- Affiliation: Department of Mathematics, Binghamton University, Binghamton, New York 13902
- MR Author ID: 65305
- Email: farrell@math.binghamton.edu
- D. Juan-Pineda
- Affiliation: Instituto de Matemáticas, UNAM Campus Morelia, Apartado Postal 61-3 (Xangari), Morelia, Michoacán, Mexico 58089
- MR Author ID: 607996
- Email: djuan@zeus.ccu.umich.mx
- K. Pearson
- Affiliation: Department of Mathematics and Computer Science, Valparaiso University, Valpa- raiso, Indiana 46383
- Email: kimberly.pearson@valpo.edu
- Received by editor(s): July 2, 1998
- Published electronically: June 28, 2000
- Additional Notes: Research partially supported by NSF grant DMS-9701746 (the second author) and a DGAPA-UNAM research grant and CONACyT # 25314E (the third author)
- © Copyright 2000 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 352 (2000), 5689-5702
- MSC (1991): Primary 19A31, 19B28, 19D35
- DOI: https://doi.org/10.1090/S0002-9947-00-02529-0
- MathSciNet review: 1694279