{"title":"su(5)-规范群的同伦类型","authors":"Tyrone Cutler, S. Theriault","doi":"10.18910/57660","DOIUrl":null,"url":null,"abstract":"Let $\\mathcal{G}_k$ be the gauge group of the principal $SU(4)$-bundle over $S^4$ with second Chern class $k$ and let $p$ be a prime. We show that there is a rational or $p$-local homotopy equivalence $\\Omega\\mathcal{G}_k\\simeq\\Omega\\mathcal{G}_{k'}$ if and only if $(60,k)=(60,k')$.","PeriodicalId":0,"journal":{"name":"","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2019-09-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"26","resultStr":"{\"title\":\"THE HOMOTOPY TYPES OF SU(5)-GAUGE GROUPS\",\"authors\":\"Tyrone Cutler, S. Theriault\",\"doi\":\"10.18910/57660\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"Let $\\\\mathcal{G}_k$ be the gauge group of the principal $SU(4)$-bundle over $S^4$ with second Chern class $k$ and let $p$ be a prime. We show that there is a rational or $p$-local homotopy equivalence $\\\\Omega\\\\mathcal{G}_k\\\\simeq\\\\Omega\\\\mathcal{G}_{k'}$ if and only if $(60,k)=(60,k')$.\",\"PeriodicalId\":0,\"journal\":{\"name\":\"\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.0,\"publicationDate\":\"2019-09-10\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"26\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.18910/57660\",\"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://doi.org/10.18910/57660","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
Let $\mathcal{G}_k$ be the gauge group of the principal $SU(4)$-bundle over $S^4$ with second Chern class $k$ and let $p$ be a prime. We show that there is a rational or $p$-local homotopy equivalence $\Omega\mathcal{G}_k\simeq\Omega\mathcal{G}_{k'}$ if and only if $(60,k)=(60,k')$.