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arXiv · 2409.04362

Compact holonomy $\mathrm{G}_2$ manifolds need not be formal

Lucía Martín-Merchán
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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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Lucía Martín-Merchán. 2024-09-06. Compact holonomy $\mathrm{G}_2$ manifolds need not be formal. https://doi.org/10.2140/gt.2026.30.1109

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