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Homotopy types of SU ( n )-gauge groups over non-spin 4-manifolds
Journal of Homotopy and Related Structures ( IF 0.7 ) Pub Date : 2019-03-12 , DOI: 10.1007/s40062-019-00233-4 Tseleung So
Journal of Homotopy and Related Structures ( IF 0.7 ) Pub Date : 2019-03-12 , DOI: 10.1007/s40062-019-00233-4 Tseleung So
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:
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。
更新日期:2019-03-12
中文翻译:
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。