Quaternionic line bundles on spin 7-manifolds
Abstract: We study quaternionic line bundles over closed, connected, spin manifolds of dimensions 6 and 7. In dimension 6, the Puppe sequence of the pair (N, N^3) gives a complete classification of the set Bun(N) of quaternionic line bundles in terms of the cohomology of the base manifold N.
In dimension 7, we consider two ways to decompose the base manifold M. First, we study the cell structure on M/M^2. Based on this, we show that the second Chern class c_2 : Bun(M) -> H^4(M;Z) is surjective. If M is simply connected and TH^3(M;Z) = 0, we obtain a partial description of the fibers over c_2 in terms of topological invariants of M. As second decomposition we consider Heegard type splittings of M. We show that the set Bun(M) can be described as a biquotient. Based on this description we see that the fibers over c_2 may differ in size
- Standort
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Deutsche Nationalbibliothek Frankfurt am Main
- Umfang
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Online-Ressource
- Anmerkungen
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Universität Freiburg, Dissertation, 2022
- Ereignis
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Veröffentlichung
- (wo)
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Freiburg
- (wer)
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Universität
- (wann)
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2022
- Urheber
- Beteiligte Personen und Organisationen
- DOI
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10.6094/UNIFR/232241
- URN
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urn:nbn:de:bsz:25-freidok-2322410
- Rechteinformation
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Open Access; Der Zugriff auf das Objekt ist unbeschränkt möglich.
- Letzte Aktualisierung
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15.08.2025, 07:32 MESZ
Datenpartner
Deutsche Nationalbibliothek. Bei Fragen zum Objekt wenden Sie sich bitte an den Datenpartner.
Beteiligte
- Gahlen, Vera Christina
- Goette, Sebastian
- Crowley, Diarmuid
- Albert-Ludwigs-Universität Freiburg. Fakultät für Mathematik und Physik
- Universität
Entstanden
- 2022
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