Combinatorics of double loop suspensions, evaluation maps and Cohen groups
文献类型：期刊论文
| 作者 | Huang, Ruizhi1; Wu, Jie2 |
| 刊名 | JOURNAL OF THE MATHEMATICAL SOCIETY OF JAPAN
 |
| 出版日期 | 2020-07-01 |
| 卷号 | 72期号:3页码:847-889 |
| 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 |
| ISSN号 | 0025-5645 |
| DOI | 10.2969/jmsj/81678167 |
| 英文摘要 | 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. |
| 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 |
| 语种 | 英语 |
| WOS记录号 | WOS:000552900200008 |
| 出版者 | MATH SOC JAPAN |
| 源URL | [http://ir.amss.ac.cn/handle/2S8OKBNM/51843]  |
| 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. |
入库方式： OAI收割
来源：数学与系统科学研究院
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