{"title":"Cyclic vs mixed homology","authors":"U. Kraehmer, Dylan Madden","doi":"10.4310/HHA.2018.V20.N1.A14","DOIUrl":null,"url":null,"abstract":"The spectral theory of the Karoubi operator due to Cuntz and Quillen is extended to general mixed (duchain) complexes, that is, chain complexes which are simultaneously cochain complexes. Connes' coboundary map B can be viewed as a perturbation of the noncommutative De Rham differential d by a polynomial in the Karoubi operator. The homological impact of such perturbations is expressed in terms of two short exact sequences.","PeriodicalId":309711,"journal":{"name":"arXiv: K-Theory and Homology","volume":null,"pages":null},"PeriodicalIF":0.0000,"publicationDate":"2016-07-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"2","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"arXiv: K-Theory and Homology","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.4310/HHA.2018.V20.N1.A14","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 2
Abstract
The spectral theory of the Karoubi operator due to Cuntz and Quillen is extended to general mixed (duchain) complexes, that is, chain complexes which are simultaneously cochain complexes. Connes' coboundary map B can be viewed as a perturbation of the noncommutative De Rham differential d by a polynomial in the Karoubi operator. The homological impact of such perturbations is expressed in terms of two short exact sequences.
京公网安备 11010802042870号
京ICP备2023020795号-1
分享
求助内容：
应助结果提醒方式：
扫码关注我们
