Compact Manifolds with Special Holonomy

by Dominic D. Joyce

Overview

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 This is the first book to be written about them, and contains much previously unpublished material which significantly improves the original constructions.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
Publication date:	09/21/2000
Series:	Oxford Mathematical Monographs
Edition description:	New Edition
Pages:	448
Product dimensions:	9.00(w) x 6.00(h) x 1.10(d)

About the Author

Lincoln College, Oxford

Table of Contents

1. Background material2. Introduction to connections, curvature and holonomy groups3. Riemannian holonomy groups4. Kähler manifolds5. The Calabi conjecture6. Calabi-Yau manifolds7. Hyperkähler manifolds8. Asymptotically locally Euclidean metrics with holonomy SU (m)9. QALE metrics with holonomy SU(m) and Sp(m)10. Introduction to the exceptional holonomy groups11. Construction of compact G₂-manifolds12. Examples of compact 7-manifolds with holonomy G₂13. Construction of compact Spin(7)-manifolds14. Examples of compact 8-manifolds with holonomy Spin(7)15. A second construction of compact 8-manifolds with holonomy Spin(7)ReferencesIndex

Editorial Reviews

Serving as both a graduate textbook on Reimannian holonomy groups and a research monograph on the exceptional holonomy groups Gc and Spin(7), this book is intended for mathematicians working in differential and Riemannian geometry and physicists working in String Theory. It's overall subject is Riemannian manifolds with special holonomy groups, especially Ricci-flat holonomy groups SU(m), Sp(m), G2, and Spin(7). Constructions and existence theorems are emphasized. Most proofs are given in full. Joyce teaches at Lincoln College. Annotation c. Book News, Inc., Portland, OR (booknews.com)

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