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On the Farrell-Jones conjecture for localising invariants

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arxiv 2111.02490 v2 pith:5GLSLMFH submitted 2021-11-03 math.KT

Ulrich Bunke , Daniel Kasprowski , Christoph Winges This is my paper · ORCID
classification math.KT
keywords categoriesconjecturefarrell-jonesgroupsadditiveamenableargumentscoefficients
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abstract

We show the Farrell-Jones conjecture with coefficients in left-exact $\infty$-categories for finitely $\mathcal{F}$-amenable groups and, more generally, Dress-Farrell-Hsiang-Jones groups. Our result subsumes and unifies arguments for the K-theory of additive categories and spherical group rings and extends it for example to categories of perfect modules over $\mathbb{E}_{1}$-ring spectra.

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  1. Survey on the Farrell-Jones Conjecture

    math.KT 2025-07 unverdicted

    The Farrell-Jones Conjecture is known for hyperbolic, CAT(0), arithmetic, and many other groups, and it implies a long list of conjectures about group rings and aspherical manifolds.

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