L2-invariants of nonuniform lattices in semisimple Lie groups

TL;DR

This paper computes L2-invariants of nonuniform lattices in semisimple Lie groups using Borel-Serre compactification, providing new estimates for Novikov-Shubin numbers and insights into L2-torsion and related conjectures.

Contribution

It introduces novel methods to estimate L2-invariants for certain lattices, advancing understanding of their spectral and torsion properties.

Findings

New estimates for Novikov-Shubin numbers

Vanishing L2-torsion for lattices with even deficiency

Applications to Gromov's Zero-in-the-Spectrum Conjecture

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.