Compact Manifolds with Special Holonomy

Erscheinungsjahr 2000
ISBN: 978-0-19-850601-0
Verlag: OUP Oxford

Buch, Englisch, 448 Seiten, Format (B × H): 161 mm x 240 mm, Gewicht: 840 g

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 This is the first book to be written about them, and contains much previously unpublished material which significantly improves the original constructions.

Autoren/Hrsg.

Joyce, Dominic D.

Joyce, Dominic David

Fachgebiete

• Mathematik | Informatik Mathematik Geometrie Differentialgeometrie
• Mathematik | Informatik Mathematik Geometrie Nicht-Euklidische Geometrie

Über Autor(innen)

University lecturer and tutorial fellow at Lincoln College, Oxford Dr D Joyce Lincoln College Oxford OX1 3DR Tel. [phone] Email: [e-mail]