On the Farrell-Jones Conjecture and its applications
Copyright policy )On the Farrell-Jones Conjecture and its applications
We present the status of the Farrell-Jones Conjecture for algebraic K-theory for a group G and arbitrary coefficient rings R. We add new groups for which the conjecture is known to be true and study inheritance properties. We discuss new applications, focussing on the Bass Conjecture, the Kaplansky Conjecture and conjectures generalizing Moody's Induction Theorem. Thus we extend the class of groups for which these conjectures are known considerably.
- Heinrich Heine University Düsseldorf Germany
- University of Münster Germany
- University of Duesseldorf Germany
\(K_1\) of group rings and orders, 19A31, Mathematics - K-Theory and Homology, \(K_0\) of group rings and orders, FOS: Mathematics, 19Dxx, K-Theory and Homology (math.KT), 19Dxx; 19A31; 19B28, Computations of higher \(K\)-theory of rings, Farrell-Jones conjecture, 19B28
\(K_1\) of group rings and orders, 19A31, Mathematics - K-Theory and Homology, \(K_0\) of group rings and orders, FOS: Mathematics, 19Dxx, K-Theory and Homology (math.KT), 19Dxx; 19A31; 19B28, Computations of higher \(K\)-theory of rings, Farrell-Jones conjecture, 19B28
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