{"title":"Eilenberg-MacLane光谱的RO(Q)梯度系数","authors":"Igor Sikora","doi":"10.1007/s40062-022-00314-x","DOIUrl":null,"url":null,"abstract":"<div><p>Let <i>Q</i> denote the cyclic group of order two. Using the Tate diagram we compute the <i>RO</i>(<i>Q</i>)-graded coefficients of Eilenberg–MacLane <i>Q</i>-spectra and describe their structure as modules over the coefficients of the Eilenberg–MacLane spectrum of the Burnside Mackey functor. If the underlying Mackey functor is a Green functor, we also obtain the multiplicative structure on the <i>RO</i>(<i>Q</i>)-graded coefficients.</p></div>","PeriodicalId":636,"journal":{"name":"Journal of Homotopy and Related Structures","volume":"17 4","pages":"525 - 568"},"PeriodicalIF":0.5000,"publicationDate":"2022-10-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s40062-022-00314-x.pdf","citationCount":"0","resultStr":"{\"title\":\"On the RO(Q)-graded coefficients of Eilenberg–MacLane spectra\",\"authors\":\"Igor Sikora\",\"doi\":\"10.1007/s40062-022-00314-x\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><p>Let <i>Q</i> denote the cyclic group of order two. Using the Tate diagram we compute the <i>RO</i>(<i>Q</i>)-graded coefficients of Eilenberg–MacLane <i>Q</i>-spectra and describe their structure as modules over the coefficients of the Eilenberg–MacLane spectrum of the Burnside Mackey functor. If the underlying Mackey functor is a Green functor, we also obtain the multiplicative structure on the <i>RO</i>(<i>Q</i>)-graded coefficients.</p></div>\",\"PeriodicalId\":636,\"journal\":{\"name\":\"Journal of Homotopy and Related Structures\",\"volume\":\"17 4\",\"pages\":\"525 - 568\"},\"PeriodicalIF\":0.5000,\"publicationDate\":\"2022-10-05\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"https://link.springer.com/content/pdf/10.1007/s40062-022-00314-x.pdf\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Journal of Homotopy and Related Structures\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://link.springer.com/article/10.1007/s40062-022-00314-x\",\"RegionNum\":4,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Homotopy and Related Structures","FirstCategoryId":"100","ListUrlMain":"https://link.springer.com/article/10.1007/s40062-022-00314-x","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
On the RO(Q)-graded coefficients of Eilenberg–MacLane spectra
Let Q denote the cyclic group of order two. Using the Tate diagram we compute the RO(Q)-graded coefficients of Eilenberg–MacLane Q-spectra and describe their structure as modules over the coefficients of the Eilenberg–MacLane spectrum of the Burnside Mackey functor. If the underlying Mackey functor is a Green functor, we also obtain the multiplicative structure on the RO(Q)-graded coefficients.
期刊介绍：
Journal of Homotopy and Related Structures (JHRS) is a fully refereed international journal dealing with homotopy and related structures of mathematical and physical sciences.
Journal of Homotopy and Related Structures is intended to publish papers on
Homotopy in the broad sense and its related areas like Homological and homotopical algebra, K-theory, topology of manifolds, geometric and categorical structures, homology theories, topological groups and algebras, stable homotopy theory, group actions, algebraic varieties, category theory, cobordism theory, controlled topology, noncommutative geometry, motivic cohomology, differential topology, algebraic geometry.
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