Localization, Whitehead groups and the Atiyah conjecture
نویسندگان
چکیده
منابع مشابه
Groups of small homological dimension and the Atiyah Conjecture
A group has homological dimension ≤ 1 if it is locally free. We prove the converse provided that G satisfies the Atiyah Conjecture about L -Betti numbers. We also show that a finitely generated elementary amenable group G of cohomological dimension ≤ 2 possesses a finite 2dimensional model for BG and in particular that G is finitely presented and the trivial ZG-module Z has a 2-dimensional reso...
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The Atiyah conjecture for a discrete group G states that the L-Betti numbers of a finite CW-complex with fundamental group G are integers if G is torsion-free, and in general that they are rational numbers with denominators determined by the finite subgroups of G. Here we establish conditions under which the Atiyah conjecture for a torsion-free group G implies the Atiyah conjecture for every fi...
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• Z(3) ^ L(2) ^ L(iy^ L(0) > HZ, localized at 2, is exact on homotopy groups. Here HZ is the integral EilenbergMac Lane spectrum, Z(0) = S°, and L(k) = X-SPS°/SP~S°. Since Z,(l) = RP°° [JTTW], exactness at Z,(0) is equivalent to the Kahn-Priddy theorem [KP]. In establishing this geometric resolution, it was found necessary to show that L(k) is projective in an appropriate sense. Regarding suspe...
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ژورنال
عنوان ژورنال: Annals of K-Theory
سال: 2018
ISSN: 2379-1691,2379-1683
DOI: 10.2140/akt.2018.3.33