L2-index theory, the Chern conjecture, and manifolds of special holonomy
L2-index theory, the Chern conjecture, and manifolds of special holonomy
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DissertationPrüfungsdatum
25.04.2014Datum der Veröffentlichung
12.12.2014Erstgutachter
Ballmann, WernerZweitgutachter
Müller, WernerMetadaten
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Inhalt
In this dissertation we study a conjecture attributed to Chern and Hopf, a generalization of Atiyah's L2-index theorem used by Gromov to prove said conjecture for Kähler manifolds, and an extension to Kähler orbifolds and all known examples of quaternionic Kähler manifolds. The study of a two-form η with values in a bundle G over a quaternionic Kähler manifold motivates us to show vanishing results for the cohomology of so5(C)-modules. We use these results to show that in certain degrees all G-valued d∇-closed forms are d∇-exact.
Schlagwörter
Indextheorie, Chernvermutung, Differentialgeometrie, Globale Analysis, Holonomie, index theory, Chern conjecture, differential geometry, global analysis, holonomy
Klassifikation (DDC)
510 MathematikHoffmann, Michael: L2-index theory, the Chern conjecture, and manifolds of special holonomy. - Bonn, 2014. - Dissertation, Rheinische Friedrich-Wilhelms-Universität Bonn.
Online-Ausgabe in bonndoc: https://nbn-resolving.org/urn:nbn:de:hbz:5n-37090
Online-Ausgabe in bonndoc: https://nbn-resolving.org/urn:nbn:de:hbz:5n-37090
@phdthesis{handle:20.500.11811/6147,
urn: https://nbn-resolving.org/urn:nbn:de:hbz:5n-37090,
author = {{Michael Hoffmann}},
title = {L2-index theory, the Chern conjecture, and manifolds of special holonomy},
school = {Rheinische Friedrich-Wilhelms-Universität Bonn},
year = 2014,
month = dec,
note = {In this dissertation we study a conjecture attributed to Chern and Hopf, a generalization of Atiyah's L2-index theorem used by Gromov to prove said conjecture for Kähler manifolds, and an extension to Kähler orbifolds and all known examples of quaternionic Kähler manifolds. The study of a two-form η with values in a bundle G over a quaternionic Kähler manifold motivates us to show vanishing results for the cohomology of so5(C)-modules. We use these results to show that in certain degrees all G-valued d∇-closed forms are d∇-exact.},
url = {https://hdl.handle.net/20.500.11811/6147}
}
urn: https://nbn-resolving.org/urn:nbn:de:hbz:5n-37090,
author = {{Michael Hoffmann}},
title = {L2-index theory, the Chern conjecture, and manifolds of special holonomy},
school = {Rheinische Friedrich-Wilhelms-Universität Bonn},
year = 2014,
month = dec,
note = {In this dissertation we study a conjecture attributed to Chern and Hopf, a generalization of Atiyah's L2-index theorem used by Gromov to prove said conjecture for Kähler manifolds, and an extension to Kähler orbifolds and all known examples of quaternionic Kähler manifolds. The study of a two-form η with values in a bundle G over a quaternionic Kähler manifold motivates us to show vanishing results for the cohomology of so5(C)-modules. We use these results to show that in certain degrees all G-valued d∇-closed forms are d∇-exact.},
url = {https://hdl.handle.net/20.500.11811/6147}
}
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