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

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.

15 pages. Comments welcome

References in corpus (2)

• A new construction of compact torsion-free $G_2$-manifolds by gluing families of Eguchi-Hanson spaces
• The ${\mathcal{L}}_B$-cohomology on compact torsion-free ${\mathrm{G}}_2$ manifolds and an application to 'almost' formality