{"title":"通过同调的n /p双曲性","authors":"Guy Boyde","doi":"10.1007/s11856-023-2563-z","DOIUrl":null,"url":null,"abstract":"Abstract We show that the homotopy groups of a Moore space P n ( p r ), where p r ≠ 2, are ℤ/ p s -hyperbolic for s ≤ r . Combined with work of Huang–Wu, Neisendorfer, and Theriault, this completely resolves the question of when such a Moore space is ℤ/ p s -hyperbolic for p ≥ 5, or when p = 2 and r ≥ 6. We also give a criterion in ordinary homology for a space to be ℤ/ p r -hyperbolic, and deduce some examples.","PeriodicalId":14661,"journal":{"name":"Israel Journal of Mathematics","volume":null,"pages":null},"PeriodicalIF":0.8000,"publicationDate":"2023-11-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"ℤ/pr-hyperbolicity via homology\",\"authors\":\"Guy Boyde\",\"doi\":\"10.1007/s11856-023-2563-z\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"Abstract We show that the homotopy groups of a Moore space P n ( p r ), where p r ≠ 2, are ℤ/ p s -hyperbolic for s ≤ r . Combined with work of Huang–Wu, Neisendorfer, and Theriault, this completely resolves the question of when such a Moore space is ℤ/ p s -hyperbolic for p ≥ 5, or when p = 2 and r ≥ 6. We also give a criterion in ordinary homology for a space to be ℤ/ p r -hyperbolic, and deduce some examples.\",\"PeriodicalId\":14661,\"journal\":{\"name\":\"Israel Journal of Mathematics\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.8000,\"publicationDate\":\"2023-11-13\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Israel Journal of Mathematics\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1007/s11856-023-2563-z\",\"RegionNum\":2,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q2\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Israel Journal of Mathematics","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1007/s11856-023-2563-z","RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 0
摘要
摘要证明了当P r≠2时，摩尔空间pn (P r)的同伦群是0 / P s -双曲的。结合Huang-Wu, Neisendorfer和Theriault的工作，这完全解决了当p≥5时，当p = 2且r≥6时，这样的摩尔空间何时为0 / p s -双曲的问题。在普通同调中，给出了空间为0 / p r -双曲的一个判据，并给出了一些例子。
Abstract We show that the homotopy groups of a Moore space P n ( p r ), where p r ≠ 2, are ℤ/ p s -hyperbolic for s ≤ r . Combined with work of Huang–Wu, Neisendorfer, and Theriault, this completely resolves the question of when such a Moore space is ℤ/ p s -hyperbolic for p ≥ 5, or when p = 2 and r ≥ 6. We also give a criterion in ordinary homology for a space to be ℤ/ p r -hyperbolic, and deduce some examples.
期刊介绍：
The Israel Journal of Mathematics is an international journal publishing high-quality original research papers in a wide spectrum of pure and applied mathematics. The prestigious interdisciplinary editorial board reflects the diversity of subjects covered in this journal, including set theory, model theory, algebra, group theory, number theory, analysis, functional analysis, ergodic theory, algebraic topology, geometry, combinatorics, theoretical computer science, mathematical physics, and applied mathematics.
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