具有平移对称性的 $SO(3)$ 反自偶方程的紧性定理
辛几何
2022-07-04 v4 数学物理
微分几何
几何拓扑
math.MP
摘要
受 Atiyah-Floer 猜想的启发，我们考虑实直线与具有柱形端的三维流形的乘积上的 反自偶瞬子。我们证明了 Gromov-Uhlenbeck 型紧性定理，即任何具有一致能量界的此类瞬子序列都有一个子序列收敛至一类奇异对象，该对象可能同时具有瞬子与全纯曲线分量。这一结果是迈向构造 Fukaya 为 Atiyah-Floer 猜想所提出的自然界定上链的第一步。
引用
@article{arxiv.1907.10205,
title = {A Compactness Theorem for $SO(3)$ Anti-Self-Dual Equation with Translation Symmetry},
author = {Guangbo Xu},
journal= {arXiv preprint arXiv:1907.10205},
year = {2022}
}
备注
71 pages, 4 figures. v2. corrected a mistake in the previous version which falsely claimed a diameter estimate. v3. shortened some arguments. v4. more details added as suggested by the referee. accepted by Advances in Mathematics