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Lifts of projective bundles and applications to string manifolds
Author(s) -
Coelho R.,
Kotschick D.
Publication year - 2021
Publication title -
bulletin of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 2.396
H-Index - 48
eISSN - 1469-2120
pISSN - 0024-6093
DOI - 10.1112/blms.12435
Subject(s) - mathematics , pure mathematics , vector bundle , lift (data mining) , cohomology , kodaira dimension , holomorphic function , projective test , manifold (fluid mechanics) , topology (electrical circuits) , dimension (graph theory) , string (physics) , combinatorics , computer science , mathematical physics , mechanical engineering , engineering , data mining
We discuss the problem of lifting projective bundles to vector bundles, giving necessary and sufficient conditions for a lift to exist both in the smooth and in the holomorphic categories. These criteria are formulated and proved in the language of topology and complex differential geometry, respectively. We also prove some results about Kähler structures on string six‐manifolds. For manifolds without any odd‐degree cohomology, one conclusion is that all such Kähler structures are projective and of negative Kodaira dimension.