Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 
 

 

The $ K$-theoretic Farrell-Jones conjecture for CAT(0)-groups


Author: Christian Wegner
Journal: Proc. Amer. Math. Soc. 140 (2012), 779-793
MSC (2000): Primary 19D10; Secondary 19A31, 19B28, 20F67
DOI: https://doi.org/10.1090/S0002-9939-2011-11150-X
Published electronically: July 14, 2011
MathSciNet review: 2869063
Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: We prove the $ K$-theoretic Farrell-Jones conjecture with (twisted) coefficients for CAT(0)-groups.


References [Enhancements On Off] (What's this?)

  • [BFJR04] Bartels, Arthur; Farrell, Tom; Jones, Lowell; Reich, Holger: On the isomorphism conjecture in algebraic $ K$-theory. Topology 43 (2004), no. 1, 157-213. MR 2030590 (2004m:19004)
  • [BL09] Bartels, Arthur; Lück, Wolfgang: The Borel Conjecture for hyperbolic and CAT(0)-groups. arXiv:0901.0442v2.
  • [BL10] Bartels, Arthur; Lück, Wolfgang: Geodesic flow for CAT(0)-groups. arXiv:1003.4630v1.
  • [BLR08] Bartels, Arthur; Lück, Wolfgang; Reich, Holger: The $ K$-theoretic Farrell-Jones conjecture for hyperbolic groups. Invent. Math. 172 (2008), no. 1, 29-70. MR 2385666 (2009c:19002)
  • [BR05] Bartels, Arthur; Reich, Holger: On the Farrell-Jones conjecture for higher algebraic $ K$-theory. J. Amer. Math. Soc. 18 (2005), no. 3, 501-545. MR 2138135 (2006e:19004)
  • [BR07] Bartels, Arthur; Reich, Holger: Coefficients for the Farrell-Jones conjecture. Adv. Math. 209 (2007), no. 1, 337-362. MR 2294225 (2008a:19002)
  • [DL98] Davis, James F.; Lück, Wolfgang: Spaces over a category and assembly maps in isomorphism conjectures in $ K$- and $ L$-theory. $ K$-Theory 15 (1998), no. 3, 201-252. MR 1659969 (99m:55004)
  • [LR05] Lück, Wolfgang; Reich, Holger: The Baum-Connes and the Farrell-Jones conjectures in $ K$- and $ L$-theory. Handbook of $ K$-theory. Vols. 1, 2, 703-842, Springer, Berlin, 2005. MR 2181833 (2006k:19012)

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC (2000): 19D10, 19A31, 19B28, 20F67

Retrieve articles in all journals with MSC (2000): 19D10, 19A31, 19B28, 20F67


Additional Information

Christian Wegner
Affiliation: Mathematisches Institut, Universität Bonn, Endenicher Allee 60, Bonn, D-53115, Germany
Email: wegner@math.uni-bonn.de

DOI: https://doi.org/10.1090/S0002-9939-2011-11150-X
Keywords: Farrell-Jones conjecture, algebraic $K$-theory of group rings, CAT(0)-groups
Received by editor(s): December 15, 2010
Published electronically: July 14, 2011
Additional Notes: The work on this paper was supported by the SFB 878 – Groups, Geometry & Actions.
Communicated by: Alexander N. Dranishnikov
Article copyright: © Copyright 2011 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.

American Mathematical Society