Asymptotic invariants of lattices in locally compact groups

descriptionPublicationkeyboard_double_arrow_right Article , Preprint 12 Jan 2023Embargo end date: 01 Jan 2018 English Publisher:MathDoc/Centre MersenneJournal:Comptes Rendus. Mathématique, volume 361, pages 375-415 (issn: 1631-073X, eissn: 1778-3569,

Copyright policy )Funded by:EC | GrDyAp

Authors: Carderi, Alessandro;

doi: 10.5802/crmath.417 , 10.48550/arxiv.1812.02133

arXiv: 1812.02133

Asymptotic invariants of lattices in locally compact groups

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Abstract

The aim of this work is to understand some of the asymptotic properties of sequences of lattices in a fixed locally compact group. In particular we will study the asymptotic growth of the Betti numbers of the lattices renormalized by the covolume and the rank gradient, the minimal number of generators also renormalized by the covolume. For doing so we will consider the ultraproduct of the sequence of actions of the locally compact group on the coset spaces and we will show how the properties of one of its cross sections are related to the asymptotic properties of the lattices.

Related Organizations

TU Dresden
Germany

Keywords

renormalization by covolume, Group Theory (math.GR), Dynamical Systems (math.DS), Discrete subgroups of Lie groups, asymptotic growth of Betti numbers, lattices, QA1-939, FOS: Mathematics, Algebraic Topology (math.AT), Mathematics - Algebraic Topology, Mathematics - Dynamical Systems, Mathematics - Group Theory, Mathematics

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