The mixed equation, defined as a combination of the anti-self-duality equation in gauge theory and Cauchy–Riemann equation in symplectic geometry, is studied. In particular, regularity and Fredholm properties are established for the solutions of this equation, and it is shown that the moduli spaces of solutions to the mixed equation satisfy a compactness property which combines Uhlenbeck and Gormov compactness theorems. The results of this paper are used in a sequel to study the Atiyah–Floer conjecture.

中文翻译：

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拉格朗日、SO(3)-瞬时和混合方程

研究了规范理论中的反自对偶方程和辛几何中的柯西-黎曼方程相结合的混合方程。特别是，对该方程的解建立了正则性和Fredholm性质，并证明了混合方程解的模空间满足结合了Uhlenbeck和Gormov紧性定理的紧性性质。这篇论文的结果被用于研究阿提亚-弗洛尔猜想的续篇中。