{"title":"2-track algebras and the Adams spectral sequence","authors":"Hans-Joachim Baues, Martin Frankland","doi":"10.1007/s40062-016-0147-x","DOIUrl":null,"url":null,"abstract":"<p>In previous work of the first author and Jibladze, the <span>\\(E_3\\)</span>-term of the Adams spectral sequence was described as a secondary derived functor, defined via secondary chain complexes in a groupoid-enriched category. This led to computations of the <span>\\(E_3\\)</span>-term using the algebra of secondary cohomology operations. In work with Blanc, an analogous description was provided for all higher terms <span>\\(E_r\\)</span>. In this paper, we introduce 2-track algebras and tertiary chain complexes, and we show that the <span>\\(E_4\\)</span>-term of the Adams spectral sequence is a tertiary Ext group in this sense. This extends the work with Jibladze, while specializing the work with Blanc in a way that should be more amenable to computations.</p>","PeriodicalId":636,"journal":{"name":"Journal of Homotopy and Related Structures","volume":"11 4","pages":"679 - 713"},"PeriodicalIF":0.5000,"publicationDate":"2016-11-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1007/s40062-016-0147-x","citationCount":"1","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Homotopy and Related Structures","FirstCategoryId":"100","ListUrlMain":"https://link.springer.com/article/10.1007/s40062-016-0147-x","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 1
Abstract
In previous work of the first author and Jibladze, the \(E_3\)-term of the Adams spectral sequence was described as a secondary derived functor, defined via secondary chain complexes in a groupoid-enriched category. This led to computations of the \(E_3\)-term using the algebra of secondary cohomology operations. In work with Blanc, an analogous description was provided for all higher terms \(E_r\). In this paper, we introduce 2-track algebras and tertiary chain complexes, and we show that the \(E_4\)-term of the Adams spectral sequence is a tertiary Ext group in this sense. This extends the work with Jibladze, while specializing the work with Blanc in a way that should be more amenable to computations.
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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