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. In the final part of the thesis, we explain an adaptation procedure for Chevalley bases of complex semisimple Lie algebras. For a given real form it yields a basis with (half)-integer structure constants that we express in terms of the root system with involution.