{"title":"\\(C_2\\)-等变拓扑模形式","authors":"Dexter Chua","doi":"10.1007/s40062-021-00297-1","DOIUrl":null,"url":null,"abstract":"<div><p>We compute the homotopy groups of the <span>\\(C_2\\)</span> fixed points of equivariant topological modular forms at the prime 2 using the descent spectral sequence. We then show that as a <span>\\({\\mathrm {TMF}}\\)</span>-module, it is isomorphic to the tensor product of <span>\\({\\mathrm {TMF}}\\)</span> with an explicit finite cell complex.</p></div>","PeriodicalId":0,"journal":{"name":"","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2022-01-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"1","resultStr":"{\"title\":\"\\\\(C_2\\\\)-equivariant topological modular forms\",\"authors\":\"Dexter Chua\",\"doi\":\"10.1007/s40062-021-00297-1\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><p>We compute the homotopy groups of the <span>\\\\(C_2\\\\)</span> fixed points of equivariant topological modular forms at the prime 2 using the descent spectral sequence. We then show that as a <span>\\\\({\\\\mathrm {TMF}}\\\\)</span>-module, it is isomorphic to the tensor product of <span>\\\\({\\\\mathrm {TMF}}\\\\)</span> with an explicit finite cell complex.</p></div>\",\"PeriodicalId\":0,\"journal\":{\"name\":\"\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.0,\"publicationDate\":\"2022-01-10\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"1\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://link.springer.com/article/10.1007/s40062-021-00297-1\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"","FirstCategoryId":"100","ListUrlMain":"https://link.springer.com/article/10.1007/s40062-021-00297-1","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
We compute the homotopy groups of the \(C_2\) fixed points of equivariant topological modular forms at the prime 2 using the descent spectral sequence. We then show that as a \({\mathrm {TMF}}\)-module, it is isomorphic to the tensor product of \({\mathrm {TMF}}\) with an explicit finite cell complex.
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