{"title":"紧凑整体性 $\\mathrm{G}_2$ 流形不必是形式的","authors":"Lucía Martín-Merchán","doi":"arxiv-2409.04362","DOIUrl":null,"url":null,"abstract":"We construct a compact, simply connected manifold with holonomy\n$\\mathrm{G}_2$ that is non-formal. We use the construction method of compact\ntorsion-free $\\mathrm{G}_2$ manifolds developed by D.D. Joyce and S.\nKarigiannis. A non-vanishing triple Massey product is obtained by arranging the\nsingular locus in a particular configuration.","PeriodicalId":501113,"journal":{"name":"arXiv - MATH - Differential Geometry","volume":"70 1","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2024-09-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Compact holonomy $\\\\mathrm{G}_2$ manifolds need not be formal\",\"authors\":\"Lucía Martín-Merchán\",\"doi\":\"arxiv-2409.04362\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"We construct a compact, simply connected manifold with holonomy\\n$\\\\mathrm{G}_2$ that is non-formal. We use the construction method of compact\\ntorsion-free $\\\\mathrm{G}_2$ manifolds developed by D.D. Joyce and S.\\nKarigiannis. A non-vanishing triple Massey product is obtained by arranging the\\nsingular locus in a particular configuration.\",\"PeriodicalId\":501113,\"journal\":{\"name\":\"arXiv - MATH - Differential Geometry\",\"volume\":\"70 1\",\"pages\":\"\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2024-09-06\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"arXiv - MATH - Differential Geometry\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/arxiv-2409.04362\",\"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 - Differential Geometry","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/arxiv-2409.04362","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
Compact holonomy $\mathrm{G}_2$ manifolds need not be formal
We construct a compact, simply connected manifold with holonomy
$\mathrm{G}_2$ that is non-formal. We use the construction method of compact
torsion-free $\mathrm{G}_2$ manifolds developed by D.D. Joyce and S.
Karigiannis. A non-vanishing triple Massey product is obtained by arranging the
singular locus in a particular configuration.
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