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On the Farrell-Jones conjecture for localising invariants

On the Farrell-Jones conjecture for localising invariants
On the Farrell-Jones conjecture for localising invariants
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.
math.KT
Cornell University
Bunke, Ulrich
b5755b35-f32f-4ec9-bb46-ded3cfd42faa
Kasprowski, Daniel
44af11b9-4d22-49f2-a6a3-04009f45b075
Winges, Christoph
347e42cd-fbb9-4dfc-80e3-84c79eb5696a
Bunke, Ulrich
b5755b35-f32f-4ec9-bb46-ded3cfd42faa
Kasprowski, Daniel
44af11b9-4d22-49f2-a6a3-04009f45b075
Winges, Christoph
347e42cd-fbb9-4dfc-80e3-84c79eb5696a

[Unknown type: UNSPECIFIED]

Record type: UNSPECIFIED

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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More information

Published date: 3 November 2021
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Keywords: math.KT

Identifiers

Local EPrints ID: 476390
URI: http://eprints.soton.ac.uk/id/eprint/476390
DOI: doi:10.48550/arXiv.2111.02490
PURE UUID: 7b3ab629-b33d-4e02-b42f-5cf3fef47372
ORCID for Daniel Kasprowski: ORCID iD orcid.org/0000-0001-5926-2206

Catalogue record

Date deposited: 19 Apr 2023 17:08
Last modified: 17 Mar 2024 04:19

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Contributors

Author: Ulrich Bunke
Author: Daniel Kasprowski ORCID iD
Author: Christoph Winges

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