Abstract
Let X be a finite aspherical CW-complex whose fundamental group π 1(X) possesses a subnormal series \({\pi_1(X) \vartriangleright G_m \vartriangleright \cdots \vartriangleright G_0}\) with a non-trivial elementary amenable group G 0. We investigate the L 2-invariants of the universal covering of such a CW-complex X. The main result is the proof of the vanishing of the L 2-torsion \({\rho^{(2)}({\tilde X})}\) under the condition that π 1(X) has semi-integral determinant. We further show that the Novikov–Shubin invariants \({\alpha_n({\tilde X})}\) are positive.
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References
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