Compact Manifolds with Special Holonomy
Book Details
Format
Hardback or Cased Book
Book Series
Oxford Mathematical Monographs
ISBN-10
0198506015
ISBN-13
9780198506010
Publisher
Oxford University Press
Imprint
Oxford University Press
Country of Manufacture
GB
Country of Publication
GB
Publication Date
Jul 20th, 2000
Print length
448 Pages
Weight
805 grams
Dimensions
24.10 x 16.10 x 2.80 cms
Ksh 38,000.00
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This is a combination of a graduate textbook on Riemannian holonomy groups, and a research monograph on compact manifolds with the exceptional holonomy groups G2 and Spin (7). It is the first book on compact manifolds with exceptional holonomy, and contains much new research material and many new examples.
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 This is the first book to be written about them, and contains much previously unpublished material which significantly improves the original constructions.
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