{"title":"衍生通用Massey产品","authors":"F. Muro","doi":"10.4310/hha.2023.v25.n1.a10","DOIUrl":null,"url":null,"abstract":"We define an obstruction to the formality of a differential graded algebra over a graded operad defined over a commutative ground ring. This obstruction lives in the derived operadic cohomology of the algebra. Moreover, it determines all operadic Massey products induced on the homology algebra, hence the name of derived universal Massey product.","PeriodicalId":55050,"journal":{"name":"Homology Homotopy and Applications","volume":null,"pages":null},"PeriodicalIF":0.8000,"publicationDate":"2021-09-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"2","resultStr":"{\"title\":\"Derived universal Massey products\",\"authors\":\"F. Muro\",\"doi\":\"10.4310/hha.2023.v25.n1.a10\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"We define an obstruction to the formality of a differential graded algebra over a graded operad defined over a commutative ground ring. This obstruction lives in the derived operadic cohomology of the algebra. Moreover, it determines all operadic Massey products induced on the homology algebra, hence the name of derived universal Massey product.\",\"PeriodicalId\":55050,\"journal\":{\"name\":\"Homology Homotopy and Applications\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.8000,\"publicationDate\":\"2021-09-03\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"2\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Homology Homotopy and Applications\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.4310/hha.2023.v25.n1.a10\",\"RegionNum\":4,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q2\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Homology Homotopy and Applications","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.4310/hha.2023.v25.n1.a10","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATHEMATICS","Score":null,"Total":0}
We define an obstruction to the formality of a differential graded algebra over a graded operad defined over a commutative ground ring. This obstruction lives in the derived operadic cohomology of the algebra. Moreover, it determines all operadic Massey products induced on the homology algebra, hence the name of derived universal Massey product.
期刊介绍：
Homology, Homotopy and Applications is a refereed journal which publishes high-quality papers in the general area of homotopy theory and algebraic topology, as well as applications of the ideas and results in this area. This means applications in the broadest possible sense, i.e. applications to other parts of mathematics such as number theory and algebraic geometry, as well as to areas outside of mathematics, such as computer science, physics, and statistics. Homotopy theory is also intended to be interpreted broadly, including algebraic K-theory, model categories, homotopy theory of varieties, etc. We particularly encourage innovative papers which point the way toward new applications of the subject.
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