$G_2$-instantons over asymptotically cylindrical manifolds

Abstract

A concrete model for a 7-dimensional gauge theory under special holonomy is proposed, within the paradigm outlined by Donaldson and Thomas, over the asymptotically cylindrical G2-manifolds provided by Kovalev's 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".

Supercedes arXiv:1101.0880v2 [math.DG]. 48 pages, 1 figure, 2 flowcharts

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