Homotopy of gauge groups over non-simply-connected five-dimensional manifolds

doi:10.1007/s11425-019-9540-3

	Homotopy of gauge groups over non-simply-connected five-dimensional manifolds
	Huang, Ruizhi
刊名	SCIENCE CHINA-MATHEMATICS
	2019-11-04
页码	32
关键词	gauge group 5-manifolds homotopy decompositions homotopy exponents homotopy groups rational homotopy theory Bott periodicity
ISSN号	1674-7283
DOI	10.1007/s11425-019-9540-3
英文摘要	Both the gauge groups and 5-manifolds are important in physics and mathematics. In this paper, we combine them together to study the homotopy aspects of gauge groups over 5-manifolds. For principal bundles over non-simply connected oriented closed 5-manifolds of certain type, we prove various homotopy decompositions of their gauge groups according to different geometric structures on the manifolds, and give the partial solution to the classification of the gauge groups. As applications, we estimate the homotopy exponents of their gauge groups, and show periodicity results of the homotopy groups of gauge groups analogous to Bott periodicity. Our treatments here are also very effective for rational gauge groups in general context, and applicable for higher dimensional manifolds.
资助项目	Postdoctoral International Exchange Program for Incoming Postdoctoral Students under Chinese Postdoctoral Council ; Chinese Postdoctoral Science Foundation[2018M631605] ; National Natural Science Foundation of China[11801544]
WOS研究方向	Mathematics
语种	英语
出版者	SCIENCE PRESS
WOS记录号	WOS:000494010700001
内容类型	期刊论文
源URL	[http://ir.amss.ac.cn/handle/2S8OKBNM/50636]
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 non-simply-connected five-dimensional manifolds[J]. SCIENCE CHINA-MATHEMATICS,2019:32.
APA	Huang, Ruizhi.(2019).Homotopy of gauge groups over non-simply-connected five-dimensional manifolds.SCIENCE CHINA-MATHEMATICS,32.
MLA	Huang, Ruizhi."Homotopy of gauge groups over non-simply-connected five-dimensional manifolds".SCIENCE CHINA-MATHEMATICS (2019):32.