On the Farrell-Jones Conjecture and its applications

2007/03/19 by Arthur Bartels, Bartels, Arthur, Wolfgang Lueck +3 · 1 citation
Mathematics · #19A31 #19B28 #19Dxx #Advanced Combinatorial Mathematics #Advanced Operator Algebra Research #FOS: Mathematics #Geometric and Algebraic Topology #K-Theory and Homology (math.KT)

paper · pdf · doi:10.48550/arxiv.math/0703548

openalex publication_date 2007/03/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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 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.

Citations

• Inheritance of Isomorphism Conjectures under colimits

Cited by

• Group pairs, coherence and Farrell--Jones Conjecture for K₀

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