The topology of instanton moduli spaces, I: The Atiyah-Jones conjecture
The topology of instanton moduli spaces, I: The Atiyah-Jones conjecture
复制标题
瞬子模空间的拓扑，I：Atiyah-Jones 猜想
DOI：
10.2307/2946532
复制
发表时间：
1993
影响因子：
4.9
通讯作者：
R. Milgram
中科院分区：
文献类型：
--
作者：
C. Boyer;J. Hurtubise;B. Mann;R. Milgram
本文研究了4-球面S4上SU（2）-瞬子模空间的整体几何和拓扑。这些瞬子模空间有着丰富的历史，并从许多角度进行了分析。最初，这些空间，我们用Mk表示，被定义为某些偏微分方程的解空间（模规范等价），即SU（2）规范理论中与杨-米尔斯泛函相关的自对偶方程。Taubes（[T1]，[T2]），Uhlenbeck [U]和其他人从这个角度成功地研究了它们。一个重要的替代方法由Ward [W]提出，他将瞬子与CP 3上的某些全纯丛联系起来，并由Atiyah和Ward在[AW]中继续。这使得分类的瞬子4美元的四元数线性代数的阿提亚，德林费尔德，希钦和马宁[ADHM]。唐纳森[D]进一步推广了这种全纯方法，他证明了这些丛是由它们对Cp 2的限制决定的，并且限制丛只需要满足在C2 R 2中的固定直线上平凡的约束。Hurtubise [Hul]然后利用这一事实来研究模空间Mk，Atiyah [A]也证明了Mk在全纯映射到循环群的理论中自然出现;后一种方法由Gravesen [G]继续。Atiyah和Jones [AJ]获得了这些模空间的第一个结果，并阐述了这些模空间的整体拓扑的基本问题。回想一下，Mk的一个元素是在$4上的主SU（2）丛上的一个联络的基规范等价类，用Pk表示，第二个陈类k，满足自对偶方程。存在到Pk中所有连接的基等价类的自然遗忘映射。Atiyah和Jones [AJ]证明了我们用Bk表示的这个目标空间是同伦等价的
In this paper we study the global geometry and topology of the moduli spaces of based SU(2)-instantons over the 4-sphere S4 . These instanton moduli spaces have a rich history and have been analyzed from many points of view. Originally these spaces, which we denote by Mk, were defined as solution spaces (modulo gauge equivalence) to certain partial differential equations, namely the self-duality equations associated to the Yang-Mills functional in SU(2) gauge theory. They have been successfully studied from this point of view by Taubes ([T1], [T2]), Uhlenbeck [U] and others. An important alternative approach was initiated by Ward [W], who related instantons to certain holomorphic bundles on CP3, and was continued by Atiyah and Ward in [AW]. This allowed the classification of instantons on $4 in terms of quaternionic linear algebra by Atiyah, Drinfeld, Hitchin and Manin [ADHM]. This holomorphic approach was further extended by Donaldson [D], who showed that these bundles were determined by their restriction to a Cp2 and that the restricted bundles only had to satisfy the constraint of being trivial on a fixed line in C2R2. Hurtubise [Hul] then exploited this fact to study the moduli spaces Mk, as did Atiyah [A] to show that Mk arise naturally in the theory of holomorphic maps into loop groups; this latter approach was continued by Gravesen [G]. Atiyah and Jones [AJ] obtained the first results and formulated the foundational questions on the global topology of these moduli spaces. Recall that an element of Mk is a based gauge-equivalence class of a connection on the principal SU(2) bundle over $4, denoted by Pk with second Chern class k, satisfying the self-duality equations. There is a natural forgetful map to the based equivalence classes of all connections in Pk. Atiyah and Jones [AJ] showed that this target space, which we denote by Bk, is homotopy equivalent
环空间的几何
DOI：
--
发表时间：
2009
期刊：
影响因子：
--
作者：
H. Irie;T. Otofuji;K.Fukaya;伊藤秀史;S.Koike;T. Funaki;金銅誠之;Yoshiaki Maeda
通讯作者：
Yoshiaki Maeda