A compact non-formal closed $G_2$ manifold with $b_1=1$

Abstract

We construct a compact manifold with a closed $G_2$ structure not admitting any torsion-free $G_2$ structure, which is non-formal and has first Betti number $b_1=1$. We develop a method of resolution for orbifolds that arise as a quotient $M/Z_2$ with $M$ a closed $G_2$ manifold under the assumption that the singular locus carries a nowhere-vanishing closed 1-form.

31 pages. v2 corrects a mistake on the definition of \hatω_1. To appear in Math Nach

References in corpus (3)

• Symplectic resolutions, Lefschetz property and formality
• A new construction of compact torsion-free $G_2$-manifolds by gluing families of Eguchi-Hanson spaces
• A compact $G_2$-calibrated manifold with first Betti number $b_1=1$