{"title":"关于Tits定理的一个辫状单群类比","authors":"Takeo Fukushi","doi":"10.55937/sut/1314883691","DOIUrl":null,"url":null,"abstract":"We extend a theorem of Tits about the fundamental groups of graphs of Coxeter groups to those of braid monoids. More precisely, we show that every self-homotopy of a word decomposes into self-homotopies each of which is inessential, a cube, a prism or a permutohedron.","PeriodicalId":38708,"journal":{"name":"SUT Journal of Mathematics","volume":"33 1","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2011-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"On a braid monoid analogue of a theorem of Tits\",\"authors\":\"Takeo Fukushi\",\"doi\":\"10.55937/sut/1314883691\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"We extend a theorem of Tits about the fundamental groups of graphs of Coxeter groups to those of braid monoids. More precisely, we show that every self-homotopy of a word decomposes into self-homotopies each of which is inessential, a cube, a prism or a permutohedron.\",\"PeriodicalId\":38708,\"journal\":{\"name\":\"SUT Journal of Mathematics\",\"volume\":\"33 1\",\"pages\":\"\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2011-01-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"SUT Journal of Mathematics\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.55937/sut/1314883691\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q4\",\"JCRName\":\"Mathematics\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"SUT Journal of Mathematics","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.55937/sut/1314883691","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"Mathematics","Score":null,"Total":0}
We extend a theorem of Tits about the fundamental groups of graphs of Coxeter groups to those of braid monoids. More precisely, we show that every self-homotopy of a word decomposes into self-homotopies each of which is inessential, a cube, a prism or a permutohedron.
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