Is the fibered Ktheoretic farrelljones conjecture true for cat(0)groups?
Yes. More precisely, both the Ltheory and Ktheory FarrellJones conjectures with coefficients in any additive category have recently been proved for CAT(0) groups:
 Arthur Bartels, Wolfgang Lück, “The Borel Conjecture for hyperbolic and CAT(0)groups”, Annals of Mathematics 175 (2012), 631–689, http://dx.doi.org/10.4007/annals.2012.175.2.5
 Christian Wegner, “The Ktheoretic FarrellJones conjecture for CAT(0)groups”, http://arxiv.org/abs/1012.3349, to appear in Proceedings of the AMS.
In Arthur Bartels, Holger Reich, “Coefficients for the FarrellJones Conjecture”, Advances in Mathematics 209:1 (2007), 337–362, it is proved that “with coefficients is stronger than fibered,” see Corollary 4.3 and Remark 4.4 on page 346.
[Edited to clarify the relation between the “with coefficients” and “fibered” versions of the FarrellJones conjectures.]

$\begingroup$ But also they proved the fibered version? $\endgroup$ – Luis Jorge Feb 22 '12 at 18:51


$\begingroup$ You are welcome, Luis! And thanks a lot, Dan! Finally, right? $\endgroup$ – Marco Varisco Feb 23 '12 at 11:26