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ISSN 1088-6850(e) ISSN 0002-9947(p)

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

Author(s): E. Berkove; F. T. Farrell; D. Juan-Pineda; K. Pearson
Journal: Trans. Amer. Math. Soc. 352 (2000), 5689-5702.
MSC (1991): Primary 19A31, 19B28, 19D35
Posted: June 28, 2000
MathSciNet review: 1694279
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Abstract:

We prove the Farrell-Jones Isomorphism Conjecture for groups acting properly discontinuously via isometries on (real) hyperbolic -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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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
Email: farrell@math.binghamton.edu

D. Juan-Pineda
Affiliation: Instituto de Matemáticas, UNAM Campus Morelia, Apartado Postal 61-3 (Xangari), Morelia, Michoacán, Mexico 58089
Email: djuan@zeus.ccu.umich.mx

K. Pearson
Affiliation: Department of Mathematics and Computer Science, Valparaiso University, Valparaiso, Indiana 46383
Email: kimberly.pearson@valpo.edu

DOI: 10.1090/S0002-9947-00-02529-0
PII: S 0002-9947(00)02529-0
Keywords: $K$-theory, discrete groups
Received by editor(s): July 2, 1998
Posted: 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 of article: Copyright 2000, American Mathematical Society

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