Homotopy of gauge groups over high-dimensional manifolds

doi:10.1017/prm.2021.1

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	Homotopy of gauge groups over high-dimensional manifolds
	Huang, Ruizhi
	2022-02-01
发表期刊	PROCEEDINGS OF THE ROYAL SOCIETY OF EDINBURGH SECTION A-MATHEMATICS
ISSN	0308-2105
卷号	152 期号:1 页码:182-208
摘要	The homotopy theory of gauge groups has received considerable attention in recent decades. In this work, we study the homotopy theory of gauge groups over some high-dimensional manifolds. To be more specific, we study gauge groups of bundles over (n - 1)-connected closed 2n-manifolds, the classification of which was determined by Wall and Freedman in the combinatorial category. We also investigate the gauge groups of the total manifolds of sphere bundles based on the classical work of James and Whitehead. Furthermore, other types of 2n-manifolds are also considered. In all the cases, we show various homotopy decompositions of gauge groups. The methods are combinations of manifold topology and various techniques in homotopy theory.
关键词	Gauge groups Homotopy suspensions Homotopy decompositions Homotopy exponents
DOI	10.1017/prm.2021.1
收录类别	SCI
语种	英语
资助项目	Postdoctoral International Exchange Program for Incoming Postdoctoral Students under Chinese Postdoctoral Council ; Chinese Postdoctoral Science Foundation[2018M631605] ; Chinese Postdoctoral Science Foundation[2019T120145] ; National Natural Science Foundation of China[11801544]
WOS研究方向	Mathematics
WOS类目	Mathematics, Applied ; Mathematics
WOS记录号	WOS:000757492400011
出版者	CAMBRIDGE UNIV PRESS
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/60069
专题	中国科学院数学与系统科学研究院
通讯作者	Huang, Ruizhi
作者单位	Chinese Acad Sci, Acad Math & Syst Sci, Inst Math, Beijing 100190, Peoples R China
推荐引用方式 GB/T 7714	Huang, Ruizhi. Homotopy of gauge groups over high-dimensional manifolds[J]. PROCEEDINGS OF THE ROYAL SOCIETY OF EDINBURGH SECTION A-MATHEMATICS,2022,152(1):182-208.
APA	Huang, Ruizhi.(2022).Homotopy of gauge groups over high-dimensional manifolds.PROCEEDINGS OF THE ROYAL SOCIETY OF EDINBURGH SECTION A-MATHEMATICS,152(1),182-208.
MLA	Huang, Ruizhi."Homotopy of gauge groups over high-dimensional manifolds".PROCEEDINGS OF THE ROYAL SOCIETY OF EDINBURGH SECTION A-MATHEMATICS 152.1(2022):182-208.