{"title":"关于无刺仙人掌，Deligne猜想和Connes-Kreimer的Hopf代数","authors":"Ralph M. Kaufmann","doi":"10.1016/j.top.2006.10.002","DOIUrl":null,"url":null,"abstract":"<div><p>Using a cell model for the little discs operad in terms of spineless cacti we give a minimal common topological operadic formalism for three a priori disparate algebraic structures: (1) a solution to Deligne’s conjecture on the Hochschild complex, (2) the Hopf algebra of Connes and Kreimer, and (3) the string topology of Chas and Sullivan.</p></div>","PeriodicalId":54424,"journal":{"name":"Topology","volume":"46 1","pages":"Pages 39-88"},"PeriodicalIF":0.0000,"publicationDate":"2007-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1016/j.top.2006.10.002","citationCount":"61","resultStr":"{\"title\":\"On spineless cacti, Deligne’s conjecture and Connes–Kreimer’s Hopf algebra\",\"authors\":\"Ralph M. Kaufmann\",\"doi\":\"10.1016/j.top.2006.10.002\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><p>Using a cell model for the little discs operad in terms of spineless cacti we give a minimal common topological operadic formalism for three a priori disparate algebraic structures: (1) a solution to Deligne’s conjecture on the Hochschild complex, (2) the Hopf algebra of Connes and Kreimer, and (3) the string topology of Chas and Sullivan.</p></div>\",\"PeriodicalId\":54424,\"journal\":{\"name\":\"Topology\",\"volume\":\"46 1\",\"pages\":\"Pages 39-88\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2007-01-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"https://sci-hub-pdf.com/10.1016/j.top.2006.10.002\",\"citationCount\":\"61\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Topology\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://www.sciencedirect.com/science/article/pii/S0040938306000565\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Topology","FirstCategoryId":"1085","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0040938306000565","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
On spineless cacti, Deligne’s conjecture and Connes–Kreimer’s Hopf algebra
Using a cell model for the little discs operad in terms of spineless cacti we give a minimal common topological operadic formalism for three a priori disparate algebraic structures: (1) a solution to Deligne’s conjecture on the Hochschild complex, (2) the Hopf algebra of Connes and Kreimer, and (3) the string topology of Chas and Sullivan.
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