{"title":"某些简单连接的 $7-$manifolds 上的自由圆作用","authors":"Fupeng Xu","doi":"arxiv-2409.04938","DOIUrl":null,"url":null,"abstract":"In this paper, we determine for which nonnegative integers $k$, $l$ and for\nwhich homotopy $7-$sphere $\\Sigma$ the manifold $kS^{2}\\times\nS^{5}\\#lS^{3}\\times S^{4}\\#\\Sigma$ admits a free smooth circle action.","PeriodicalId":501271,"journal":{"name":"arXiv - MATH - Geometric Topology","volume":"37 1","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2024-09-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Free circle actions on certain simply connected $7-$manifolds\",\"authors\":\"Fupeng Xu\",\"doi\":\"arxiv-2409.04938\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"In this paper, we determine for which nonnegative integers $k$, $l$ and for\\nwhich homotopy $7-$sphere $\\\\Sigma$ the manifold $kS^{2}\\\\times\\nS^{5}\\\\#lS^{3}\\\\times S^{4}\\\\#\\\\Sigma$ admits a free smooth circle action.\",\"PeriodicalId\":501271,\"journal\":{\"name\":\"arXiv - MATH - Geometric Topology\",\"volume\":\"37 1\",\"pages\":\"\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2024-09-08\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"arXiv - MATH - Geometric Topology\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/arxiv-2409.04938\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"arXiv - MATH - Geometric Topology","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/arxiv-2409.04938","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
Free circle actions on certain simply connected $7-$manifolds
In this paper, we determine for which nonnegative integers $k$, $l$ and for
which homotopy $7-$sphere $\Sigma$ the manifold $kS^{2}\times
S^{5}\#lS^{3}\times S^{4}\#\Sigma$ admits a free smooth circle action.
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