Compact holonomy $\mathrm{G}_2$ manifolds need not be formal
Differential Geometry
2026-05-06 v1 Algebraic Topology
Abstract
We construct a compact, simply connected manifold with holonomy that is non-formal. We use the construction method of compact torsion-free 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.
Keywords
Cite
@article{arxiv.2409.04362,
title = {Compact holonomy $\mathrm{G}_2$ manifolds need not be formal},
author = {Lucía Martín-Merchán},
journal= {arXiv preprint arXiv:2409.04362},
year = {2026}
}
Comments
15 pages. Comments welcome