Homotopy types of SU(n)-gauge groups over non-spin 4-manifolds

IF 0.5 4区数学

Journal of Homotopy and Related Structures Pub Date : 2019-03-12 DOI:10.1007/s40062-019-00233-4

Tseleung So

引用次数: 4

Abstract

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.

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非自旋4流形上的SU(n)规范群的同伦类型

让M是一个可定向的，单连通的，闭合的，不自旋的?设\({\mathcal {G}}_k(M)\)为M上具有二阶Chern类的主g束的规群\(k\in {\mathbb {Z}}\)。已知\({\mathcal {G}}_k(M)\)的同伦类型是由\({\mathcal {G}}_k({\mathbb {C}}{\mathbb {P}}^2)\)的同伦类型决定的。本文研究了\({\mathcal {G}}_k({\mathbb {C}}{\mathbb {P}}^2)\)在\(G=SU(n)\)对规范群的同伦类型进行部分分类时的性质。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Journal of Homotopy and Related Structures Mathematics-Geometry and Topology

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期刊介绍： Journal of Homotopy and Related Structures (JHRS) is a fully refereed international journal dealing with homotopy and related structures of mathematical and physical sciences. Journal of Homotopy and Related Structures is intended to publish papers on Homotopy in the broad sense and its related areas like Homological and homotopical algebra, K-theory, topology of manifolds, geometric and categorical structures, homology theories, topological groups and algebras, stable homotopy theory, group actions, algebraic varieties, category theory, cobordism theory, controlled topology, noncommutative geometry, motivic cohomology, differential topology, algebraic geometry.