Closed $\mathrm{G}_2$ structures on compact manifolds satisfying the known topological obstructions to holonomy $\mathrm{G}_2$ metrics

Lucía Martín-Merchán

paper

Closed $G_{2}$ structures on compact manifolds satisfying the known topological obstructions to holonomy $G_{2}$ metrics

arXiv:2508.12658

Abstract

We construct new compact manifolds endowed with closed $G_{2}$ structures that satisfy the topological properties found by Joyce and Baraglia for the existence of a torsion-free $G_{2}$ structure in the same cohomology class. Those manifolds arise as resolutions of orbifolds of the form $M / Z_{2}$ , where $M$ itself does not admit any torsion-free $G_{2}$ structure. We develop an equivariant resolution procedure for closed $G_{2}$ orbifolds with $Z_{2}$ isotropy, and analyze some topological properties of the resolved manifolds, including their first Pontryagin class and certain triple Massey products.

arXiv comment50 pages. Comments welcome!

Closed G2​ structures on compact manifolds satisfying the known topological obstructions to holonomy G2​ metrics

Abstract

Closed $G_{2}$ structures on compact manifolds satisfying the known topological obstructions to holonomy $G_{2}$ metrics