{"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}
引用次数: 0
Abstract
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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