Compact manifolds with special holonomy
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). Th...
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| Formato: | Livro |
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Oxford University Press
2000
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| _version_ | 1826298481279500288 |
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| author | Joyce, D |
| author_facet | Joyce, D |
| author_sort | Joyce, D |
| collection | OXFORD |
| description | 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 This is the first book to be written about them, and contains much previously unpublished material which significantly improves the original constructions. |
| first_indexed | 2024-03-07T04:47:30Z |
| format | Book |
| id | oxford-uuid:d3cf444f-8dab-43d7-974c-f5e4ae9f0a08 |
| institution | University of Oxford |
| last_indexed | 2024-03-07T04:47:30Z |
| publishDate | 2000 |
| publisher | Oxford University Press |
| record_format | dspace |
| spelling | oxford-uuid:d3cf444f-8dab-43d7-974c-f5e4ae9f0a082022-03-27T08:13:51ZCompact manifolds with special holonomyBookhttp://purl.org/coar/resource_type/c_2f33uuid:d3cf444f-8dab-43d7-974c-f5e4ae9f0a08Symplectic Elements at OxfordOxford University Press2000Joyce, DThe 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. |
| spellingShingle | Joyce, D Compact manifolds with special holonomy |
| title | Compact manifolds with special holonomy |
| title_full | Compact manifolds with special holonomy |
| title_fullStr | Compact manifolds with special holonomy |
| title_full_unstemmed | Compact manifolds with special holonomy |
| title_short | Compact manifolds with special holonomy |
| title_sort | compact manifolds with special holonomy |
| work_keys_str_mv | AT joyced compactmanifoldswithspecialholonomy |