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Finite group extensions and the Atiyah conjecture
Journal of The American Mathematical Society
The Atiyah conjecture for a discrete group G states that the L^2-Betti numbers of a finite CW-complex with fundamental group G are integers if G is torsion-free and are rational with denominators determined by the finite subgroups of G in general. Here we establish conditions under which the Atiyah conjecture for a group G implies the Atiyah conjecture for every finite extension of G. The most important requirement is that the cohomology H^*(G,Z/p) is isomorphic to the cohomology of the p-adicdoi:10.1090/s0894-0347-07-00561-9 fatcat:jfsiqjckazdg7b2sxpirv4sjou