Combinatorics of double loop suspensions, evaluation maps and Cohen groups

doi:10.2969/jmsj/81678167

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	Combinatorics of double loop suspensions, evaluation maps and Cohen groups
	Huang, Ruizhi 1; Wu, Jie 2
	2020-07-01
发表期刊	JOURNAL OF THE MATHEMATICAL SOCIETY OF JAPAN
ISSN	0025-5645
卷号	72 期号:3 页码:847-889
摘要	We reformulate Milgram's model of a double loop suspension in terms of a preoperad of posets, each stage of which is the poset of all ordered partitions of a finite set. Using this model, we give a combinatorial model for the evaluation map and use it to study the Cohen representation for the group of homotopy classes of maps between double loop suspensions. Demonstrating the general theory, we recover Wu's shuffle relations and further provide a type of secondary relations in Cohen groups by using Toda brackets. In particular, we prove certain maps are null-homotopic by combining our relations and the classical James-Hopf invariants.
关键词	double loop suspensions homotopy exponents Barratt-Cohen conjecture Milgram's model preoperad permutohedra evaluation maps bi-Delta-groups Cohen groups shuffle relations
DOI	10.2969/jmsj/81678167
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 ; Chinese Postdoctoral Science Foundation[2018M631605] ; Chinese Postdoctoral Science Foundation[2019T120145] ; National Natural Science Foundation of China[11801544] ; National Natural Science Foundation of China[11971144] ; High-level Scientific Research Foundation of Hebei Province[13113093]
WOS研究方向	Mathematics
WOS类目	Mathematics
WOS记录号	WOS:000552900200008
出版者	MATH SOC JAPAN
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/51844
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	1.Chinese Acad Sci, Acad Math & Syst Sci, Inst Math, Beijing 100190, Peoples R China 2.Hebei Normal Univ, Sch Math Sci, 20 Rd East 2nd Ring South, Shijiazhuang 050024, Hebei, Peoples R China
推荐引用方式 GB/T 7714	Huang, Ruizhi,Wu, Jie. Combinatorics of double loop suspensions, evaluation maps and Cohen groups[J]. JOURNAL OF THE MATHEMATICAL SOCIETY OF JAPAN,2020,72(3):847-889.
APA	Huang, Ruizhi,&Wu, Jie.(2020).Combinatorics of double loop suspensions, evaluation maps and Cohen groups.JOURNAL OF THE MATHEMATICAL SOCIETY OF JAPAN,72(3),847-889.
MLA	Huang, Ruizhi,et al."Combinatorics of double loop suspensions, evaluation maps and Cohen groups".JOURNAL OF THE MATHEMATICAL SOCIETY OF JAPAN 72.3(2020):847-889.