Miguel Ángel Marco Buzunáriz, A. Romero, Jose Divasón
{"title":"Effective Homology of Universal Covers","authors":"Miguel Ángel Marco Buzunáriz, A. Romero, Jose Divasón","doi":"10.1145/3614408.3614414","DOIUrl":null,"url":null,"abstract":"We present an algorithm for constructing the effective homology for the universal cover of simplicial sets with effective homology, provided that a nilpotency condition holds. This can be useful for computing higher homotopy groups, since this process can be seen as the first step in the Whitehead tower. Our algorithm can be applied to some spaces satisfying a particular condition. We also present implementations of this method in SageMath and Kenzo.","PeriodicalId":41965,"journal":{"name":"ACM Communications in Computer Algebra","volume":"57 1","pages":"47 - 50"},"PeriodicalIF":0.4000,"publicationDate":"2023-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"ACM Communications in Computer Algebra","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1145/3614408.3614414","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"MATHEMATICS, APPLIED","Score":null,"Total":0}
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Abstract
We present an algorithm for constructing the effective homology for the universal cover of simplicial sets with effective homology, provided that a nilpotency condition holds. This can be useful for computing higher homotopy groups, since this process can be seen as the first step in the Whitehead tower. Our algorithm can be applied to some spaces satisfying a particular condition. We also present implementations of this method in SageMath and Kenzo.
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