L2–invariants of nonuniform lattices in semisimple Lie groups

Kammeyer, Holger

doi:10.2140/agt.2014.14.2475

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$L^{2}$–invariants of nonuniform lattices in semisimple Lie groups

Holger Kammeyer

Algebraic & Geometric Topology 14 (2014) 2475–2509

DOI: 10.2140/agt.2014.14.2475

Abstract

We compute $L^{2}$ –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 $L^{2}$ –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 $L^{2}$ –torsion of measure-equivalent groups.

Keywords

$L^2$–invariants, lattices, Borel–Serre compactification

Mathematical Subject Classification 2010

Primary: 22E40

Secondary: 57Q10, 53C35

References

Publication

Received: 5 September 2013

Accepted: 17 December 2013

Published: 28 August 2014

Authors

Holger Kammeyer
Mathematisches Institut Universität Bonn Endenicher Allee 60 D-53115 Bonn Germany
http://www.math.uni-bonn.de/people/kammeyer/

Volume 14, issue 4 (2014)