Compact Manifolds with Special Holonomy

By: Dominic D. Joyce

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Hardcover | 1 August 2000

At a Glance

Hardcover
452 Pages

Dimensions(cm)
23.39 x 15.6 x 2.54

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 This is the first book to be written about them, and contains much previously unpublished material which significantly improves the original constructions.

Industry Reviews

The book is written in a very clear and understandable way, with careful explanation of the main ideas and many remarks and comments, and it includes systematic suggestions for further reading ... It can be warmly recommended to mathematicians (in geometry and global analysis, in particular) as well as to physicists interested in string theory. EMS The first part is a very effective introduction to basic notions and results of modern differential geometry ... This book is highly recommended for people who are interested in the very recent developments of differential geometry and its relationships with present research in theoretical physics. Zentralblatt MATH

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You Can Find This Book In

Non-Fiction Mathematics Geometry Differential & Riemannian Geometry Science Physics Algebraic Geometry Topology Non-Euclidean Geometry

Background material
Introduction to connections, curvature and holonomy groups
Riemannian holonomy groups
Kahler manifolds
The Calabi conjecture
Calabi-Yau manifolds
Hyperkahler manifolds
Asymptotically locally Euclidean metrics with holonomy SU (m)
QALE metrics with holonomy SU(m) and Sp(m)
Introduction to the exceptional holonomy groups
Construction of compact G2-manifolds
Examples of compact 7-manifolds with holonomy G2
Construction of compact Spin(7)-manifolds
Examples of compact 8-manifolds with holonomy Spin(7)
A second construction of compact 8-manifolds with holonomy Spin(7)
References
Index
Table of Contents provided by Publisher. All Rights Reserved.

Compact Manifolds with Special Holonomy

At a Glance

Hardcover

Industry Reviews

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How to return your order

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