Constructing compact 8-manifolds with holonomy Spin(7) from Calabi-Yau orbifolds
Compact Riemannian 7- and 8-manifolds with holonomy G(2) arid Spin(7) were first constructed by the author in 1994-5, by resolving orbifolds T-7/Gamma and T-8/Gamma. This paper describes a new construction of compact 8-manifolds with holonomy Spin(7). We start with a Calabi-Yau 4-orbifold Y with iso...
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| Format: | Conference item |
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2001
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| _version_ | 1826289755924463616 |
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| author | Joyce, D |
| author_facet | Joyce, D |
| author_sort | Joyce, D |
| collection | OXFORD |
| description | Compact Riemannian 7- and 8-manifolds with holonomy G(2) arid Spin(7) were first constructed by the author in 1994-5, by resolving orbifolds T-7/Gamma and T-8/Gamma. This paper describes a new construction of compact 8-manifolds with holonomy Spin(7). We start with a Calabi-Yau 4-orbifold Y with isolated singularities of a special kind. We divide by an antiholomorphic involution a of Y to get a real 8-orbifold Z = Y/<sigma>. Then we resolve tire singularities of Z to get a compact 8-manifold M, which has metrics with holonomy Spin(7). Manifolds constructed in this way typically have large fourth Betti number b(4)(M).</sigma> |
| first_indexed | 2024-03-07T02:33:44Z |
| format | Conference item |
| id | oxford-uuid:a817ae63-34e0-4d26-9d1c-103582a11857 |
| institution | University of Oxford |
| last_indexed | 2024-03-07T02:33:44Z |
| publishDate | 2001 |
| record_format | dspace |
| spelling | oxford-uuid:a817ae63-34e0-4d26-9d1c-103582a118572022-03-27T02:59:02ZConstructing compact 8-manifolds with holonomy Spin(7) from Calabi-Yau orbifoldsConference itemhttp://purl.org/coar/resource_type/c_5794uuid:a817ae63-34e0-4d26-9d1c-103582a11857Symplectic Elements at Oxford2001Joyce, DCompact Riemannian 7- and 8-manifolds with holonomy G(2) arid Spin(7) were first constructed by the author in 1994-5, by resolving orbifolds T-7/Gamma and T-8/Gamma. This paper describes a new construction of compact 8-manifolds with holonomy Spin(7). We start with a Calabi-Yau 4-orbifold Y with isolated singularities of a special kind. We divide by an antiholomorphic involution a of Y to get a real 8-orbifold Z = Y/<sigma>. Then we resolve tire singularities of Z to get a compact 8-manifold M, which has metrics with holonomy Spin(7). Manifolds constructed in this way typically have large fourth Betti number b(4)(M).</sigma> |
| spellingShingle | Joyce, D Constructing compact 8-manifolds with holonomy Spin(7) from Calabi-Yau orbifolds |
| title | Constructing compact 8-manifolds with holonomy Spin(7) from Calabi-Yau orbifolds |
| title_full | Constructing compact 8-manifolds with holonomy Spin(7) from Calabi-Yau orbifolds |
| title_fullStr | Constructing compact 8-manifolds with holonomy Spin(7) from Calabi-Yau orbifolds |
| title_full_unstemmed | Constructing compact 8-manifolds with holonomy Spin(7) from Calabi-Yau orbifolds |
| title_short | Constructing compact 8-manifolds with holonomy Spin(7) from Calabi-Yau orbifolds |
| title_sort | constructing compact 8 manifolds with holonomy spin 7 from calabi yau orbifolds |
| work_keys_str_mv | AT joyced constructingcompact8manifoldswithholonomyspin7fromcalabiyauorbifolds |