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
- Location
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Deutsche Nationalbibliothek Frankfurt am Main
- Extent
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Online-Ressource
- Notes
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Universität Freiburg, Dissertation, 2022
- Event
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Veröffentlichung
- (where)
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Freiburg
- (who)
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Universität
- (when)
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2022
- Creator
- Contributor
- DOI
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10.6094/UNIFR/232241
- URN
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urn:nbn:de:bsz:25-freidok-2322410
- Rights
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Open Access; Der Zugriff auf das Objekt ist unbeschränkt möglich.
- Last update
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25.03.2025, 1:45 PM CET
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Deutsche Nationalbibliothek. If you have any questions about the object, please contact the data provider.
Associated
- Gahlen, Vera Christina
- Goette, Sebastian
- Crowley, Diarmuid
- Albert-Ludwigs-Universität Freiburg. Fakultät für Mathematik und Physik
- Universität
Time of origin
- 2022
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Generalizing holomorphic bundles to almost complex manifolds
On the Growth of Dimension of Harmonic Spaces of Semipositive Line Bundles over Manifolds
Normal forms for Dirac–Jacobi bundles and splitting theorems for Jacobi structures
Complex line bundles over simplicial complexes
Spin(7)-manifolds of cohomogeneity one
Heights for line bundles on arithmetic surfaces
Hodge index theorem for adelic line bundles
Partially ample line bundles on toric varieties
Stability and Hermitian-Einstein metrics for vector bundles on framed manifolds
The area preserving Willmore flow and local maximizers of the Hawking mass in asymptotically Schwarzschild manifolds
Positivity of line bundles and Newton-Okounkov bodies
Positive line bundles over the irreducible quantum flag manifolds
Generalizing holomorphic bundles to almost complex manifolds
On the Growth of Dimension of Harmonic Spaces of Semipositive Line Bundles over Manifolds
Normal forms for Dirac–Jacobi bundles and splitting theorems for Jacobi structures
Complex line bundles over simplicial complexes
Spin(7)-manifolds of cohomogeneity one
Heights for line bundles on arithmetic surfaces
Hodge index theorem for adelic line bundles
Partially ample line bundles on toric varieties
Stability and Hermitian-Einstein metrics for vector bundles on framed manifolds
The area preserving Willmore flow and local maximizers of the Hawking mass in asymptotically Schwarzschild manifolds