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Moduli Spaces of $$G_{2}$$ G 2 -Instantons and Spin (7)-Instantons on Product Manifolds
Annales Henri Poincaré ( IF 1.4 ) Pub Date : 2020-07-17 , DOI: 10.1007/s00023-020-00938-w
Yuanqi Wang

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:

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

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\(X_times S ^ {1} \)\(G_ {2} \) -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。
更新日期:2020-07-17
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