Bryant–Salamon G2 manifolds and coassociative fibrations
| Autor: | Spiro Karigiannis, Jason D. Lotay |
|---|---|
| Rok vydání: | 2021 |
| Předmět: |
Pure mathematics
010102 general mathematics Holonomy Fibration General Physics and Astronomy Harmonic (mathematics) Conical surface 01 natural sciences Cone (topology) Product (mathematics) 0103 physical sciences Line (geometry) Calibrated geometry 010307 mathematical physics Geometry and Topology 0101 mathematics Mathematical Physics Mathematics |
| Zdroj: | Journal of Geometry and Physics. 162:104074 |
| ISSN: | 0393-0440 |
| DOI: | 10.1016/j.geomphys.2020.104074 |
| Popis: | Bryant–Salamon constructed three 1-parameter families of complete manifolds with holonomy G 2 which are asymptotically conical to a holonomy G 2 cone. For each of these families, including their asymptotic cone, we construct a fibration by asymptotically conical and conically singular coassociative 4-folds. We show that these fibrations are natural generalizations of the following three well-known coassociative fibrations on R 7 : the trivial fibration by 4-planes, the product of the standard Lefschetz fibration of ℂ 3 with a line, and the Harvey–Lawson coassociative fibration. In particular, we describe coassociative fibrations of the bundle of anti-self-dual 2-forms over the 4-sphere S 4 , and the cone on ℂ P 3 , whose smooth fibres are T ∗ S 2 , and whose singular fibres are R 4 ∕ { ± 1 } . We relate these fibrations to hypersymplectic geometry, Donaldson’s work on Kovalev–Lefschetz fibrations, harmonic 1-forms and the Joyce–Karigiannis construction of holonomy G 2 manifolds, and we construct vanishing cycles and associative “thimbles” for these fibrations. |
| Databáze: | OpenAIRE |
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