{"title":"路径颤振的组合模型","authors":"Manuel Rivera, Samson Saneblidze","doi":"10.1007/s40062-018-0216-4","DOIUrl":null,"url":null,"abstract":"<p>We introduce the abstract notion of a necklical set in order to describe a functorial combinatorial model of the path fibration over the geometric realization of a path connected simplicial set. In particular, to any path connected simplicial set <i>X</i> we associate a necklical set <span>\\({\\widehat{{\\varvec{\\Omega }}}}X\\)</span> such that its geometric realization <span>\\(|{\\widehat{{\\varvec{\\Omega }}}}X|\\)</span>, a space built out of gluing cubical cells, is homotopy equivalent to the based loop space on |<i>X</i>| and the differential graded module of chains <span>\\(C_*({\\widehat{{\\varvec{\\Omega }}}}X)\\)</span> is a differential graded associative algebra generalizing Adams’ cobar construction.</p>","PeriodicalId":0,"journal":{"name":"","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2018-09-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1007/s40062-018-0216-4","citationCount":"6","resultStr":"{\"title\":\"A combinatorial model for the path fibration\",\"authors\":\"Manuel Rivera, Samson Saneblidze\",\"doi\":\"10.1007/s40062-018-0216-4\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<p>We introduce the abstract notion of a necklical set in order to describe a functorial combinatorial model of the path fibration over the geometric realization of a path connected simplicial set. In particular, to any path connected simplicial set <i>X</i> we associate a necklical set <span>\\\\({\\\\widehat{{\\\\varvec{\\\\Omega }}}}X\\\\)</span> such that its geometric realization <span>\\\\(|{\\\\widehat{{\\\\varvec{\\\\Omega }}}}X|\\\\)</span>, a space built out of gluing cubical cells, is homotopy equivalent to the based loop space on |<i>X</i>| and the differential graded module of chains <span>\\\\(C_*({\\\\widehat{{\\\\varvec{\\\\Omega }}}}X)\\\\)</span> is a differential graded associative algebra generalizing Adams’ cobar construction.</p>\",\"PeriodicalId\":0,\"journal\":{\"name\":\"\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.0,\"publicationDate\":\"2018-09-29\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"https://sci-hub-pdf.com/10.1007/s40062-018-0216-4\",\"citationCount\":\"6\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://link.springer.com/article/10.1007/s40062-018-0216-4\",\"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/s40062-018-0216-4","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
We introduce the abstract notion of a necklical set in order to describe a functorial combinatorial model of the path fibration over the geometric realization of a path connected simplicial set. In particular, to any path connected simplicial set X we associate a necklical set \({\widehat{{\varvec{\Omega }}}}X\) such that its geometric realization \(|{\widehat{{\varvec{\Omega }}}}X|\), a space built out of gluing cubical cells, is homotopy equivalent to the based loop space on |X| and the differential graded module of chains \(C_*({\widehat{{\varvec{\Omega }}}}X)\) is a differential graded associative algebra generalizing Adams’ cobar construction.
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