L2–invariants of nonuniform lattices in semisimple Lie groups

Kammeyer, Holger¹

¹Mathematisches Institut, Universität Bonn, Endenicher Allee 60, D-53115 Bonn, Germany

Algebraic and Geometric Topology, Tome 14 (2014) no. 4, pp. 2475-2509

Résumé

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.

Détail

DOI : 10.2140/agt.2014.14.2475

Classification : 22E40, 57Q10, 53C35
Keywords: $L^2$–invariants, lattices, Borel–Serre compactification

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