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Journal of the American Mathematical Society
Journal of the American Mathematical Society
ISSN 1088-6834(online) ISSN 0894-0347(print)

 

The Farrell-Jones Conjecture for cocompact lattices in virtually connected Lie groups


Authors: A. Bartels, F. T. Farrell and W. Lück
Journal: J. Amer. Math. Soc. 27 (2014), 339-388
MSC (2010): Primary 18F25, 19A31, 19B28, 19G24, 22E40, 57N99
Published electronically: January 15, 2014
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Abstract: Let $ G$ be a cocompact lattice in a virtually connected Lie group or the fundamental group of a three-dimensional manifold. We prove the $ K$- and $ L$-theoretic Farrell-Jones Conjectures for $ G$.


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Additional Information

A. Bartels
Affiliation: Westfälische Wilhelms-Universität Münster, Mathematicians Institut,Einsteinium. 62, D-48149 Münster, Germany
Email: bartelsa@math.uni-muenster.de

F. T. Farrell
Affiliation: Department of Mathematics, Suny, Binghamton, New York, New York 13902
Email: farrell@math.binghamton.edu

W. Lück
Affiliation: Mathematicians Institut der Universität Bonn, Endenicher Allee 60, 53115 Bonn, Germany
Email: wolfgang.lueck@him.uni-bonn.de

DOI: http://dx.doi.org/10.1090/S0894-0347-2014-00782-7
PII: S 0894-0347(2014)00782-7
Keywords: Farrell-Jones Conjecture, $K$- and $L$-theory of group rings, cocompact lattices in virtually connected Lie groups, fundamental groups of $3$-manifolds.
Received by editor(s): January 3, 2011
Received by editor(s) in revised form: April 16, 2013
Published electronically: January 15, 2014
Article copyright: © Copyright 2014 American Mathematical Society