G2–instantons over asymptotically cylindrical manifolds

Sá Earp, Henrique¹

¹ Imperial College London, London SW7 2AZ, UK, Universidade Estadual de Campinas (Unicamp), São Paulo, Brazil

Geometry & topology, Tome 19 (2015) no. 1, pp. 61-111.

Résumé

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”.

Détail

DOI : 10.2140/gt.2015.19.61

Classification : 53C07, 58J35, 53C29
Keywords: gauge theory, $G_2$–instantons

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