\(G_{2}\)-instantons over asymptotically cylindrical. (English) Zbl 1312.53044
Summary: A concrete model for a \(7\)-dimensional gauge theory under special holonomy is proposed, within the paradigm of Donaldson and Thomas, over the asymptotically cylindrical \(G_2\)-manifolds provided by Kovalev’s solution to a noncompact version of the Calabi conjecture. One obtains a solution to the \(G_2\)-instanton equation from the associated Hermitian Yang-Mills problem, to which the methods of Simpson et al are applied, subject to a crucial asymptotic stability assumption over the “boundary at infinity”.
MSC:
| 53C07 | Special connections and metrics on vector bundles (Hermite-Einstein, Yang-Mills) |
| 58J35 | Heat and other parabolic equation methods for PDEs on manifolds |
| 53C29 | Issues of holonomy in differential geometry |
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