{"title":"Infinite families of higher torsion in the homotopy groups of Moore spaces","authors":"Steven Amelotte, F. Cohen, Y. Luo","doi":"10.2140/agt.2023.23.2389","DOIUrl":null,"url":null,"abstract":"We give a refinement of the stable Snaith splitting of the double loop space of a Moore space and use it to construct infinite $v_1$-periodic families of elements of order $p^{r+1}$ in the homotopy groups of mod $p^r$ Moore spaces. For odd primes $p$, our splitting implies that the homotopy groups of the mod $p^{r+1}$ Moore spectrum are summands of the unstable homotopy groups of each mod $p^r$ Moore space.","PeriodicalId":50826,"journal":{"name":"Algebraic and Geometric Topology","volume":"87 1","pages":""},"PeriodicalIF":0.6000,"publicationDate":"2021-11-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Algebraic and Geometric Topology","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.2140/agt.2023.23.2389","RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 0
Abstract
We give a refinement of the stable Snaith splitting of the double loop space of a Moore space and use it to construct infinite $v_1$-periodic families of elements of order $p^{r+1}$ in the homotopy groups of mod $p^r$ Moore spaces. For odd primes $p$, our splitting implies that the homotopy groups of the mod $p^{r+1}$ Moore spectrum are summands of the unstable homotopy groups of each mod $p^r$ Moore space.