L2-invariants of nonuniform lattices in semisimple Lie groups

Abstract

We compute L2-invariants of certain nonuniform lattices in semisimple Lie groups by means of the Borel-Serre compactification of arithmetically defined locally symmetric spaces. The main results give new estimates for Novikov-Shubin numbers and vanishing L2-torsion for lattices in groups with even deficiency. We discuss applications to Gromov's Zero-in-the-Spectrum Conjecture as well as to a proportionality conjecture for the L2-torsion of measure equivalent groups.

35 pages, 2 figures

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• On the torsion in the cohomology of arithmetic hyperbolic 3-manifolds
• L^2-Betti Numbers of Locally Compact Groups
• Entropy, Determinants, and L2-Torsion