Compact Manifolds with Special Holonomy

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 This is the first book to be written about them, and contains much previously unpublished material which significantly improves the original constructions.

Author: Dominic D. Joyce
Publisher: OUP Oxford
Published: 09/21/2000
Pages: 448
Binding Type: Hardcover
Weight: 1.74lbs
Size: 9.30h x 6.30w x 1.19d
ISBN: 9780198506010

Review Citation(s):
Scitech Book News 09/01/2001 pg. 50

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