Lagrangians, SO(3)-Instantons and Mixed Equation

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...

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Published inGeometric and functional analysis Vol. 34; no. 3; pp. 659 - 732
Main Authors Daemi, Aliakbar, Fukaya, Kenji, Lipyanskiy, Maksim
Format Journal Article
LanguageEnglish
Published Cham Springer International Publishing 01.06.2024
Springer Nature B.V
Subjects
Analysis
Cauchy-Riemann equations
Gauge theory
Instantons
Mathematics
Mathematics and Statistics
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ISSN1016-443X
1420-8970
DOI10.1007/s00039-024-00677-8

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Summary: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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ISSN:1016-443X
1420-8970
DOI:10.1007/s00039-024-00677-8