拉格朗日、SO(3)-等式和混合方程

IF 2.4 1区数学 Q1 MATHEMATICS

Geometric and Functional Analysis Pub Date : 2024-05-02 DOI:10.1007/s00039-024-00677-8

Aliakbar Daemi, Kenji Fukaya, Maksim Lipyanskiy

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引用次数: 0

摘要

研究了混合方程，它被定义为规规理论中反自偶方程与交点几何中考奇-黎曼方程的结合。特别是，为该方程的解建立了正则性和弗雷德霍姆性质，并证明混合方程的解的模空间满足紧凑性性质，该性质结合了乌伦贝克紧凑性定理和戈尔莫夫紧凑性定理。本文的结果将用于研究 Atiyah-Floer 猜想的续集。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

Lagrangians, SO(3)-Instantons and Mixed Equation

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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 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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来源期刊

Geometric and Functional Analysis 数学-数学

CiteScore

3.70

自引率

4.50%

发文量

审稿时长

6-12 weeks

期刊介绍： Geometric And Functional Analysis (GAFA) publishes original research papers of the highest quality on a broad range of mathematical topics related to geometry and analysis. GAFA scored in Scopus as best journal in "Geometry and Topology" since 2014 and as best journal in "Analysis" since 2016. Publishes major results on topics in geometry and analysis. Features papers which make connections between relevant fields and their applications to other areas.