Let M be an orientable, simply-connected, closed, non-spin 4-manifold and let \({\mathcal {G}}_k(M)\) be the gauge group of the principal G-bundle over M with second Chern class \(k\in {\mathbb {Z}}\). It is known that the homotopy type of \({\mathcal {G}}_k(M)\) is determined by the homotopy type of \({\mathcal {G}}_k({\mathbb {C}}{\mathbb {P}}^2)\). In this paper we investigate properties of \({\mathcal {G}}_k({\mathbb {C}}{\mathbb {P}}^2)\) when \(G=SU(n)\) that partly classify the homotopy types of the gauge groups.

中文翻译：

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非旋转4流形上SU（n）规群的同伦型

令M为可定向的，简单连接的，封闭的，非旋转的4流形，令\（{\ mathcal {G}} _ k（M）\）为主体G束在M上具有第二个Chern的尺度组类\（k \ in {\ mathbb {Z}} \）。已知\（{\ mathcal {G}} _ k（M）\）的同伦类型由\（{\ mathcal {G}} _ k（{\ mathbb {C}} {\ mathbb {P}} ^ 2）\）。在本文中，我们研究\（{= mathcal {G}} _ k（{\ mathbb {C}} {\ mathbb {P}} ^ 2）\）的属性，当\（G = SU（n）\）部分对规范组的同伦类型进行分类。