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arXiv · 1903.05526

${\rm Spin}(7)$-Instantons from evolution equations

Andrew Clarke·Gonçalo Oliveira
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Abstract

In this paper we study ${\rm Spin}(7)$-instantons on asymptotically conical ${\rm Spin}(7)$-orbifolds (and manifolds) obtained by filling in certain squashed $3$-Sasakian $7$-manifolds. We construct a $1$-parameter family of explicit ${\rm Spin}(7)$-instantons. Taking the parameter to infinity, the family (a) bubbles off an ASD connection in directions transverse to a certain Cayley submanifold $Z$, (b) away from $Z$ smoothly converges to a limit ${\rm Spin}(7)$-instanton that extends across $Z$ onto a topologically distinct bundle, (c) satisfies an energy conservation law for the instantons and the bubbles concentrated on $Z$, and (d) determines a Fueter section, in the sense of Donaldson and Segal, Haydys and Walpuski.

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Andrew Clarke, Gonçalo Oliveira. 2019-03-13. ${\rm Spin}(7)$-Instantons from evolution equations. https://arxiv.org/abs/1903.05526

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