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arXiv · 2109.07038

Lagrangians, SO(3)-instantons and mixed equation

Aliakbar Daemi·Kenji Fukaya·Maksim Lipyanskiy
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Abstract

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.

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Aliakbar Daemi, Kenji Fukaya, Maksim Lipyanskiy. 2021-09-15. Lagrangians, SO(3)-instantons and mixed equation. https://arxiv.org/abs/2109.07038

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