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Compact Manifolds with Special Holonomy
Abstract
The book starts with a thorough introduction to connections and holonomy groups, and to Riemannian, complex and Kähler geometry. Then the Calabi conjecture is proved and used to deduce the existence of compact manifolds with holonomy SU(m) (Calabi-Yau manifolds) and Sp(m) (hyperkähler manifolds). These are constructed and studied using complex algebraic geometry. The second half of the book is devoted to constructions of compact 7- and 8-manifolds with the exceptional holonomy groups 92 and Spin(7). Many new examples are given, and their Betti numbers calculated. The first known examples of these manifolds were discovered by the author in 1993-5. This is the first book to be written about them, and contains much previously unpublished material which significantly improves the original constructions.
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Citations
Cited by
Twisted connected sums and special Riemannian holonomy
Kovalev, A. (2003) · Journal für die reine und angewandte Mathematik (Crelles Journal) · doi:10.1515/crll.2003.097 · Cited by 192
Deformations of asymptotically cylindrical G2-manifolds
NORDSTRÖM, J. (2008) · Mathematical Proceedings of the Cambridge Philosophical Society · doi:10.1017/s0305004108001333 · Cited by 21
MODULI SPACES OF TOPOLOGICAL CALIBRATIONS, CALABI–YAU, HYPERKÄHLER, G2and SPIN(7) STRUCTURES
GOTO, R. (2004) · International Journal of Mathematics · doi:10.1142/s0129167x04002296 · Cited by 15
Metadata
- Authors
- Joyce, D. D.
- Publisher
- Oxford University PressOxford
- Published
- 2000-07-20
- OpenAlex
- W1941650215
- Cited by
- 963
- References
- 0
- FWCI
- 20.08
- Type
- book
- Language
- en
- Open access
- closed
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