L^2-Invariants of Finite Aspherical CW-Complexes

Abstract

Let $X$ be a finite aspherical CW-complex whose fundamental group ${\pi }_1(X)$ possesses a subnormal series ${\pi }_1(X)⊳G_m⊳...⊳G_0$ with a non-trivial elementary amenable group $G_0$. We investigate the $L^2$-invariants of the universal covering of such a CW-complex $X$. We show that the Novikov-Shubin invariants ${\alpha }_n(\tilde{X})$ are positive. We further prove that the $L^2$-torsion ${\rho }^{(2)}(\tilde{X})$ vanishes if ${\pi }_1(X)$ has semi-integral determinant.

11 pages