Is the fibered K-theoretic farrell-jones conjecture true for cat(0)-groups?


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:

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.]

  • $\begingroup$ But also they proved the fibered version? $\endgroup$ – Luis Jorge Feb 22 '12 at 18:51
  • $\begingroup$ Yes, see the paragraph I added above. $\endgroup$ – Marco Varisco Feb 22 '12 at 19:05
  • $\begingroup$ You are welcome, Luis! And thanks a lot, Dan! Finally, right? $\endgroup$ – Marco Varisco Feb 23 '12 at 11:26

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