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Mathematics > Dynamical Systems

arXiv:1812.09014 (math)
[Submitted on 21 Dec 2018 (v1), last revised 15 Aug 2019 (this version, v2)]

Title:Rigidity sequences, Kazhdan sets and group topologies on the integers

Authors:Catalin Badea, Sophie Grivaux, Etienne Matheron
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Abstract:We study the relationships between three different classes of sequences (or sets) of integers, namely rigidity sequences, Kazhdan sequences (or sets) and nullpotent sequences. We prove that rigidity sequences are non-Kazhdan and nullpotent, and that all other implications are false. In particular, we show by probabilistic means that there exist sequences of integers which are both nullpotent and Kazhdan. Moreover, using Baire category methods, we provide general criteria for a sequence of integers to be a rigidity sequence. Finally, we give a new proof of the existence of rigidity sequences which are dense in $\mathbb{Z}$ for the Bohr topology, a result originally due to Griesmer.
Comments: 28 p. To appear in the Journal d'Analyse Mathématique
Subjects: Dynamical Systems (math.DS); Functional Analysis (math.FA); Group Theory (math.GR)
Cite as: arXiv:1812.09014 [math.DS]
  (or arXiv:1812.09014v2 [math.DS] for this version)
  https://doi.org/10.48550/arXiv.1812.09014

Submission history

From: Sophie Grivaux [view email]
[v1] Fri, 21 Dec 2018 09:38:47 UTC (45 KB)
[v2] Thu, 15 Aug 2019 19:53:42 UTC (46 KB)
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