Is the fibered K-theoretic farrell-jones conjecture true for cat(0)-groups?
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Yes. More precisely, both the L-theory and K-theory Farrell-Jones 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 K-theoretic Farrell-Jones 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 Farrell-Jones 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 Farrell-Jones conjectures.]
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$\begingroup$ But also they proved the fibered version? $\endgroup$ Commented Feb 22, 2012 at 18:51
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$\begingroup$ Yes, see the paragraph I added above. $\endgroup$ Commented Feb 22, 2012 at 19:05
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$\begingroup$ You are welcome, Luis! And thanks a lot, Dan! Finally, right? $\endgroup$ Commented Feb 23, 2012 at 11:26