Annals of K-Theory
- Ann. K-Theory
- Volume 3, Number 1 (2018), 33-53.
Localization, Whitehead groups and the Atiyah conjecture
Let be the -group of square matrices over which are not necessarily invertible but induce weak isomorphisms after passing to Hilbert space completions. Let be the division closure of in the algebra of operators affiliated to the group von Neumann algebra. Let be the smallest class of groups which contains all free groups and is closed under directed unions and extensions with elementary amenable quotients. Let be a torsionfree group which belongs to . Then we prove that is isomorphic to . Furthermore we show that is a skew field and hence is the abelianization of the multiplicative group of units in .
Ann. K-Theory, Volume 3, Number 1 (2018), 33-53.
Received: 22 February 2016
Revised: 4 November 2016
Accepted: 27 November 2016
First available in Project Euclid: 20 December 2017
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Primary: 19B99: None of the above, but in this section
Secondary: 16S85: Rings of fractions and localizations [See also 13B30] 22D25: $C^*$-algebras and $W^*$-algebras in relation to group representations [See also 46Lxx]
Lück, Wolfgang; Linnell, Peter. Localization, Whitehead groups and the Atiyah conjecture. Ann. K-Theory 3 (2018), no. 1, 33--53. doi:10.2140/akt.2018.3.33. https://projecteuclid.org/euclid.akt/1513774601