Abstract
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 .
Citation
Wolfgang Lück. Peter Linnell. "Localization, Whitehead groups and the Atiyah conjecture." Ann. K-Theory 3 (1) 33 - 53, 2018. https://doi.org/10.2140/akt.2018.3.33
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