Annals of K-Theory

On the Farrell–Jones conjecture for algebraic $K$-theory of spaces: the Farrell–Hsiang method

Mark Ullmann and Christoph Winges

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Abstract

We prove the Farrell–Jones conjecture for algebraic K -theory of spaces for virtually poly- -groups. For this, we transfer the “Farrell–Hsiang method” from the linear case to categories of equivariant, controlled retractive spaces.

Article information

Source
Ann. K-Theory, Volume 4, Number 1 (2019), 57-138.

Dates
Received: 4 October 2017
Revised: 10 September 2018
Accepted: 27 September 2018
First available in Project Euclid: 9 April 2019

Permanent link to this document
https://projecteuclid.org/euclid.akt/1554775255

Digital Object Identifier
doi:10.2140/akt.2019.4.57

Mathematical Reviews number (MathSciNet)
MR3936015

Zentralblatt MATH identifier
07051947

Subjects
Primary: 19D10: Algebraic $K$-theory of spaces
Secondary: 18F25: Algebraic $K$-theory and L-theory [See also 11Exx, 11R70, 11S70, 12- XX, 13D15, 14Cxx, 16E20, 19-XX, 46L80, 57R65, 57R67] 57Q10: Simple homotopy type, Whitehead torsion, Reidemeister-Franz torsion, etc. [See also 19B28]

Keywords
algebraic $K\mkern-2mu$-theory of spaces Farrell–Jones conjecture poly-$\mathbb Z$-groups

Citation

Ullmann, Mark; Winges, Christoph. On the Farrell–Jones conjecture for algebraic $K$-theory of spaces: the Farrell–Hsiang method. Ann. K-Theory 4 (2019), no. 1, 57--138. doi:10.2140/akt.2019.4.57. https://projecteuclid.org/euclid.akt/1554775255


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