#### Volume 19, issue 1 (2015)

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$G_2$–instantons over asymptotically cylindrical manifolds

### Henrique N Sá Earp

Geometry & Topology 19 (2015) 61–111
##### Abstract

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”.

##### Keywords
gauge theory, $G_2$–instantons
##### Mathematical Subject Classification 2010
Primary: 53C07
Secondary: 58J35, 53C29