Coefficients for the Farrell¿Jones Conjecture

By Arthur Bartels, H. Reich. 2005

65 citations recorded by the source corpus.

Abstract 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 K - or 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.

Subfields: Algebra and Number Theory, Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/ae0f92035cd09b911e122b21073a24868d669cdf

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In Algebra and Number Theory

In Geometry and Topology

In Mathematical Physics

Citations in the corpus

The Farrell–Jones conjecture for arbitrary lattices in virtually connected Lie groups (2014, methodology): “We will deal with the more general version with coefficients in additive categories and with finite wreath products, see [3,8], and [7, Definition 6.”
The Farrell-Jones Conjecture for cocompact lattices in virtually connected Lie groups (2011, background): “2 are formulated and analyzed in [5], [12].”
On the Farrell–Jones Conjecture and its applications (2007, methodology): “Coefficient rings with operation In the setup developed so far, we have not dealt with the more general version developed in Bartels–Reich [8], where one fixes a group and considers an additive category with G-action.”
The Borel Conjecture for hyperbolic and CAT(0)-groups (2009, methodology): “The Farrell-Jones Conjectures have been generalized to include group rings RG over arbitrary rings [4], and further to twisted group rings which are best treated using the language of actions of G on additive categories [5], [11].”