{"title":"Stabilizing and commuting cochains","authors":"Max Karoubi","doi":"10.1016/S0764-4442(01)02118-8","DOIUrl":null,"url":null,"abstract":"<div><p>As it is well known in <em>K</em>-theory, stabilization of matrices enables them to commute “up to homotopy”. The purpose of this short paper is to describe an analogous philosophy for cochains on a space. It is in fact a direct application of a paper of Henri Cartan [1], together with a new idea of stabilization for cochains, similar to matrices. The application below may be also deduced from a paper of J. Halperin and J. Stasheff [2] by a quite different method. This paper is part of a joint project with P. Baum about the cohomology of homogeneous spaces. Since it has some independent interest, it might be useful to present it on its own right.</p></div>","PeriodicalId":100300,"journal":{"name":"Comptes Rendus de l'Académie des Sciences - Series I - Mathematics","volume":"333 8","pages":"Pages 769-771"},"PeriodicalIF":0.0000,"publicationDate":"2001-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1016/S0764-4442(01)02118-8","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Comptes Rendus de l'Académie des Sciences - Series I - Mathematics","FirstCategoryId":"1085","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0764444201021188","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
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Abstract
As it is well known in K-theory, stabilization of matrices enables them to commute “up to homotopy”. The purpose of this short paper is to describe an analogous philosophy for cochains on a space. It is in fact a direct application of a paper of Henri Cartan [1], together with a new idea of stabilization for cochains, similar to matrices. The application below may be also deduced from a paper of J. Halperin and J. Stasheff [2] by a quite different method. This paper is part of a joint project with P. Baum about the cohomology of homogeneous spaces. Since it has some independent interest, it might be useful to present it on its own right.
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