m at h . K T ] 2 7 O ct 2 00 5 COEFFICIENTS FOR THE FARRELL - JONES CONJECTURE
نویسنده
چکیده
We introduce the Farrell-Jones Conjecture with coefficients in an additive category with G-action. This is a variant of the Farrell-Jones Conjecture about the algebraic Kor L-Theory of a group ring RG. It allows to treat twisted group rings and crossed product rings. The conjecture with coefficients is stronger than the original conjecture but it has better inheritance properties. Since known proofs using controlled algebra carry over to the set-up with coefficients we obtain new results about the original Farrell-Jones Conjecture. The conjecture with coefficients implies the fibered version of the Farrell-Jones Conjecture.
منابع مشابه
9 M ay 2 00 7 Inheritance of Isomorphism Conjectures un - der colimits Arthur Bartels , Siegfried Echterhoff and Wolfgang Lück
We investigate when Isomorphism Conjectures, such as the ones due to BaumConnes, Bost and Farrell-Jones, are stable under colimits of groups over directed sets (with not necessarily injective structure maps). We show in particular that both the K-theoretic Farrell-Jones Conjecture and the Bost Conjecture with coefficients hold for those groups for which Higson, Lafforgue and Skandalis have disp...
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We show that the Fibered Isomorphism Conjecture of T. Farrell and L. Jones holds for various mapping class groups. In many cases, we explicitly calculate the lower algebraic K-groups, showing that they do not always vanish.
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