Anibal M. Medina-Mardones, Andrea Pizzi, Paolo Salvatore
{"title":"多简链和构型空间","authors":"Anibal M. Medina-Mardones, Andrea Pizzi, Paolo Salvatore","doi":"10.1007/s40062-024-00344-7","DOIUrl":null,"url":null,"abstract":"<div><p>We define an <span>\\(E_\\infty \\)</span>-coalgebra structure on the chains of multisimplicial sets. Our primary focus is on the surjection chain complexes of McClure-Smith, for which we construct a zig-zag of complexity preserving quasi-isomorphisms of <span>\\(E_\\infty \\)</span>-coalgebras relating them to both the singular chains on configuration spaces and the Barratt–Eccles chain complexes.</p></div>","PeriodicalId":0,"journal":{"name":"","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-05-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s40062-024-00344-7.pdf","citationCount":"0","resultStr":"{\"title\":\"Multisimplicial chains and configuration spaces\",\"authors\":\"Anibal M. Medina-Mardones, Andrea Pizzi, Paolo Salvatore\",\"doi\":\"10.1007/s40062-024-00344-7\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><p>We define an <span>\\\\(E_\\\\infty \\\\)</span>-coalgebra structure on the chains of multisimplicial sets. Our primary focus is on the surjection chain complexes of McClure-Smith, for which we construct a zig-zag of complexity preserving quasi-isomorphisms of <span>\\\\(E_\\\\infty \\\\)</span>-coalgebras relating them to both the singular chains on configuration spaces and the Barratt–Eccles chain complexes.</p></div>\",\"PeriodicalId\":0,\"journal\":{\"name\":\"\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.0,\"publicationDate\":\"2024-05-09\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"https://link.springer.com/content/pdf/10.1007/s40062-024-00344-7.pdf\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://link.springer.com/article/10.1007/s40062-024-00344-7\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"","FirstCategoryId":"100","ListUrlMain":"https://link.springer.com/article/10.1007/s40062-024-00344-7","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
We define an \(E_\infty \)-coalgebra structure on the chains of multisimplicial sets. Our primary focus is on the surjection chain complexes of McClure-Smith, for which we construct a zig-zag of complexity preserving quasi-isomorphisms of \(E_\infty \)-coalgebras relating them to both the singular chains on configuration spaces and the Barratt–Eccles chain complexes.
求助内容：
应助结果提醒方式：
京公网安备 11010802042870号
