Compact Manifolds with Special Holonomy

Hardcover | February 15, 2004

byDominic David Joyce

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The book starts with a thorough introduction to connections and holonomy groups, and to Riemannian, complex and Kahler 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) (hyperkahlermanifolds). 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 firstknown 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 This is the first book to be written about them, and contains much previously unpublished material which significantly improves the original constructions.

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From the Publisher

The book starts with a thorough introduction to connections and holonomy groups, and to Riemannian, complex and Kahler 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) (hyperkahlermanifolds). These are constructed and studied usin...

University lecturer and tutorial fellow at Lincoln College, Oxford Dr D Joyce Lincoln College Oxford OX1 3DR Tel. 01865 279800 Email: dominic.joyce@lincoln.ox.ac.uk
Format:HardcoverPublished:February 15, 2004Publisher:Oxford University PressLanguage:English

The following ISBNs are associated with this title:

ISBN - 10:0198506015

ISBN - 13:9780198506010

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