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Profinite invariants of arithmetic groups

Kammeyer, Holger; Kionke, Steffen; Raimbault, Jean; Sauer, Roman

Abstract:
We prove that the sign of the Euler characteristic of arithmetic groups with the congruence subgroup property is determined by the profinite completion. In contrast, we construct examples showing that this is not true for the Euler characteristic itself and that the sign of the Euler characteristic is not profinite among general residually finite groups of type F. Our methods imply similar results for ℓ$^{2}$ -torsion as well as a strong profiniteness statement for Novikov–Shubin invariants.

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Verlagsausgabe §
DOI: 10.5445/IR/1000126958
Veröffentlicht am 30.11.2020
Cover der Publikation
Zugehörige Institution(en) am KIT Institut für Algebra und Geometrie (IAG)
Publikationstyp Zeitschriftenaufsatz
Publikationsjahr 2020
Sprache Englisch
Identifikator ISSN: 2050-5094
KITopen-ID: 1000126958
Erschienen in Forum of mathematics / Sigma
Band 8
Seiten Art.-Nr.: e54
Schlagwörter profinite rigidity, arithmetic groups, l2-invariants
Nachgewiesen in Scopus
Web of Science
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