Dokument: Profinite Invariance and Bounded Cohomology
| Titel: | Profinite Invariance and Bounded Cohomology | |||||||
| URL für Lesezeichen: | https://docserv.uni-duesseldorf.de/servlets/DocumentServlet?id=73966 | |||||||
| URN (NBN): | urn:nbn:de:hbz:061-20260720-135129-8 | |||||||
| Kollektion: | Dissertationen | |||||||
| Sprache: | Englisch | |||||||
| Dokumententyp: | Wissenschaftliche Abschlussarbeiten » Dissertation | |||||||
| Medientyp: | Text | |||||||
| Autor: | Echtler, Daniel [Autor] | |||||||
| Dateien: |
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| Beitragende: | Kammeyer, Holger [Gutachter] Kionke, Steffen [Gutachter] | |||||||
| Dewey Dezimal-Klassifikation: | 500 Naturwissenschaften und Mathematik » 510 Mathematik | |||||||
| Beschreibung: | We study to what extent the second real bounded cohomology is a profinite invariant. First, we construct pairs of residually finite groups with isomorphic profinite completions where one has non-vanishing second real bounded cohomology while the other one does not. These examples are lattices in higher rank simple Lie groups.
Using Galois cohomology, we actually classify all higher rank Lie groups admitting such examples. The complete list consists of those groups isogenous to SO⁰(n,2) for n ⩾ 6 and the exceptional groups E₆⁽⁻¹⁴⁾ and E₇⁽⁻²⁵⁾. For the classification, we use results from number theory and class field theory, Margulis arithmeticity and adelic superrigidity, as well as the classifications of semisimple algebraic groups and semisimple Lie groups. Additionally, we introduce and study the notion of natural profinite invariants. These are functorial group invariants sending every Grothendieck pair to an isomorphism. We prove that there is no logical connection to the usual notion of profinite invariants. For this purpose we give examples of functorial invariants that are profinite, but not naturally profinite, as well as the other way around. Moreover, we also prove that the second (exact) bounded cohomology is not a natural profinite invariant. | |||||||
| Lizenz: |  Dieses Werk ist lizenziert unter einer Creative Commons Namensnennung 4.0 International Lizenz | |||||||
| Fachbereich / Einrichtung: | Mathematisch- Naturwissenschaftliche Fakultät » WE Mathematik » Algebra und Zahlentheorie | |||||||
| Dokument erstellt am: | 20.07.2026 | |||||||
| Dateien geändert am: | 20.07.2026 | |||||||
| Promotionsantrag am: | 07.04.2026 | |||||||
| Datum der Promotion: | 16.07.2026 |
