Moduli spaces of $G_{2}$ and $Spin(7)-$instantons on product manifolds

Yuanqi Wang

paper

Moduli spaces of $G_{2}$ and $S p in (7) -$ instantons on product manifolds

arXiv:1803.05899

Abstract

Let $X$ be a closed $6 -$ dimensional manifold with a half-closed $S U (3) -$ structure. On the product manifold $X \times S^{1}$ , with respect to the product $G_{2} -$ structure and on a pullback vector bundle from $X$ , we show that any $G_{2} -$ instanton is equivalent to a Hermitian Yang-Mills connection on $X$ via a "broken gauge". This result reveals the topological type of the moduli of $G_{2} -$ instantons on $X \times S^{1}$ . In dimension $8$ , similar result holds for moduli of $S p in (7) -$ instantons. A generalization and an example are given.

23 pages, 1 figure. Improved presentation. Final version to appear in Annales Henri Poincaré

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$G_{2}$ -instantons on the 7-sphere

Moduli spaces of G2​ and Spin(7)−instantons on product manifolds

Abstract

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Cited by in corpus (1)

Moduli spaces of $G_{2}$ and $S p in (7) -$ instantons on product manifolds