Compact Manifolds with Special Holonomy (Oxford Mathematical Monographs)

出版者:Oxford University Press, USA

作者:Dominic D. Joyce

页数:448

出版时间:2000-09-21

价格:USD 170.00

装帧:Hardcover

isbn号码:9780198506010

图书标签:紧流形数学

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The book starts with a thorough introduction to connections and holonomy groups, and to Riemannian, complex and Kahler 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) (hyperkahler 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 This is the first book to be written about them, and contains much previously unpublished material, which significantly improves the original constructions.