Compact Manifolds with Special Holonomy

Compact Manifolds with Special Holonomy

by Dominic D. Joyce
Pub. Date:
Oxford University Press, USA


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 This is the first book to be written about them, and contains much previously unpublished material which significantly improves the original constructions.

Product Details

ISBN-13: 9780198506010
Publisher: Oxford University Press, USA
Publication date: 07/28/2000
Series: Oxford Mathematical Monographs Series
Edition description: New Edition
Pages: 448
Product dimensions: 9.00(w) x 6.00(h) x 1.10(d)

Table of Contents

1. Background material
2. Introduction to connections, curvature and holonomy groups
3. Riemannian holonomy groups
4. Kähler manifolds
5. The Calabi conjecture
6. Calabi-Yau manifolds
7. Hyperkähler manifolds
8. Asymptotically locally Euclidean metrics with holonomy SU (m)
9. QALE metrics with holonomy SU(m) and Sp(m)
10. Introduction to the exceptional holonomy groups
11. Construction of compact G[2-manifolds
12. Examples of compact 7-manifolds with holonomy G[2
13. Construction of compact Spin(7)-manifolds
14. Examples of compact 8-manifolds with holonomy Spin(7)
15. A second construction of compact 8-manifolds with holonomy Spin(7)

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