Compact Manifolds with Special Holonomy

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Dominic David Joyce (University Lecturer and Tutorial Fellow, University Lecturer and Tutorial Fellow, Lincoln College, Oxford)

Compact Manifolds with Special Holonomy

Dominic David Joyce (University Lecturer and Tutorial Fellow, University Lecturer and Tutorial Fellow, Lincoln College, Oxford)

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English

Oxford University Press
01 August 2000

Geometry; Differential & Riemannian geometry; Physics

Series: Oxford Mathematical Monographs

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This is the first book to be written about them, and contains much previously unpublished material which significantly improves the original constructions.

By: Dominic David Joyce (University Lecturer and Tutorial Fellow University Lecturer and Tutorial Fellow Lincoln College Oxford)
Imprint: Oxford University Press
Country of Publication: United Kingdom
Dimensions: Height: 241mm, Width: 161mm, Spine: 28mm
Weight: 1g
ISBN: 9780198506010
ISBN 10: 0198506015
Series: Oxford Mathematical Monographs
Pages: 448
Publication Date: 01 August 2000
Audience: Professional and scholarly , Undergraduate
Format: Hardback
Publisher's Status: Active

University lecturer and tutorial fellow at Lincoln College, Oxford Dr D Joyce Lincoln College Oxford OX1 3DR Tel. 01865 279800 Email: dominic.joyce@lincoln.ox.ac.uk

Reviews for Compact Manifolds with Special Holonomy

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