Let X be a closed 6-dimensional manifold with a half-closed SU(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 Spin(7)-instantons. A generalization and an example are given.

中文翻译：

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产品流形上的$$ G_ {2} $$ G 2 -Instantons和Spin（7）-Instantons的模空间

令X为具有半封闭SU（3）结构的封闭6维流形。在乘积流形（{X \ times S ^ {1} \）上，相对于乘积\（G_ {2} \）-结构，以及在X的回拉向量束上，我们证明任何\（G_ {2 } \） -instanton等效于X上通过“折断规”的Hermitian Yang-Mills连接。该结果揭示了\（X_times S ^ {1} \）上\（G_ {2} \） -实例的模的拓扑类型。在维度8中，自旋（7）-瞬间的模量具有相似的结果。给出了一个概括和一个例子。