L2-index theory, the Chern conjecture, and manifolds of special holonomy

Hoffmann, Michael

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L²-index theory, the Chern conjecture, and manifolds of special holonomy

Hoffmann, M. (2017). L²-index theory, the Chern conjecture, and manifolds of special holonomy. PhD Thesis, Rheinische Friedrich-Wilhelms-Universität Bonn, Bonn.

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Item Permalink: https://hdl.handle.net/21.11116/0000-0004-0C94-8 Version Permalink: https://hdl.handle.net/21.11116/0000-0009-0107-E

Genre: Thesis

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https://hdl.handle.net/20.500.11811/6147 (Any fulltext) Open Access status unknown

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Hoffmann, Michael¹, Author

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1Max Planck Institute for Mathematics, Max Planck Society, ou_3029201

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Abstract: 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.

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Language(s): eng - English

Dates: Accepted: 2017

Publication Status: Accepted / In Press

Pages: 78 p.

Publishing info: Bonn : Rheinische Friedrich-Wilhelms-Universität Bonn

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Identifiers: URN: https://nbn-resolving.org/urn:nbn:de:hbz:5n-37090

Degree: PhD

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