{"title":"Comparing orthogonal calculus and calculus with Reality","authors":"Niall Taggart","doi":"10.1007/s00209-024-03545-1","DOIUrl":null,"url":null,"abstract":"<p>We show that there exists a suitable <span>\\(C_2\\)</span>-fixed points functor from calculus with Reality to the orthogonal calculus of Weiss which recovers orthogonal calculus “up to a shift” in an analogous way with the recovery of real topological <i>K</i>-theory from Atiyah’s <i>K</i>-theory with Reality via appropriate <span>\\(C_2\\)</span>-fixed points.</p>","PeriodicalId":18278,"journal":{"name":"Mathematische Zeitschrift","volume":"37 1","pages":""},"PeriodicalIF":1.0000,"publicationDate":"2024-07-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Mathematische Zeitschrift","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1007/s00209-024-03545-1","RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 0
Abstract
We show that there exists a suitable \(C_2\)-fixed points functor from calculus with Reality to the orthogonal calculus of Weiss which recovers orthogonal calculus “up to a shift” in an analogous way with the recovery of real topological K-theory from Atiyah’s K-theory with Reality via appropriate \(C_2\)-fixed points.
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