On the Farrell-Jones Conjecture and its applications

Arthur Bartels, Wolfgang Lück, Holger Reich

Type: Article

Publication Date: 2007-10-28

Citations: 69

DOI: https://doi.org/10.1112/jtopol/jtm008

Abstract

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 we study inheritance properties. We discuss new applications, focussing on the Bass Conjecture, the Kaplansky Conjecture, and conjectures generalizing Moody's Induction Theorem. Thus, we considerably extend the class of groups for which these conjectures are known.

Locations

arXiv (Cornell University) - View - PDF
Journal of Topology - View

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Works Cited by This (68)

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+	Idempotents in complex group rings: theorems of Zalesskii and Bass revisited	1998	Marc Burger Alain Valette
+	Hyperelementary assembly for K-theory of virtually abelian groups	2005	Frank Quinn
+ PDF Chat	Moody's induction theorem	1988	Gerald Cliff Alfred Weiss
+	Fields and rings	1969	Irving Kaplansky
+	Exact sequences in the algebraic theory of surgery	1981	Andrew Ranicki
+ PDF Chat	p-adic Entropy and a p-adic Fuglede–Kadison Determinant	2009	Christopher Deninger
+ PDF Chat	Recognition of subgroups of direct products of hyperbolic groups	2003	Martin R. Bridson Charles F. Miller
+	The Algebraic Structure of Group Rings	1977	D. S. Passman
+	Linear Representations of Finite Groups	1977	Jean-Pierre Serre
+	Progrès récents sur la conjecture de Baum-Connes. Contribution de Vincent Lafforgue	2000	Georges Skandalis