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Search: authors:"Goncalo Oliveira"

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SU(2) \(^2\) -invariant \(G_2\) -instantons

We initiate the systematic study of \(G_2\)-instantons with SU(2)\(^2\)-symmetry. As well as developing foundational theory, we give existence, non-existence and classification results for these instantons. We particularly focus on \(\mathbb {R}^4\times S^3\) with its two explicitly known distinct holonomy \(G_2\) metrics, which have different volume growths at infinity...