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

2025/08/18 by Lucía Martín‐Merchán, Martín-Merchán, Lucía
Mathematics · Physics and Astronomy · #53C15 #53C29 #55P62 #55S30 #Advanced Differential Geometry Research #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds

paper · pdf · doi:10.48550/arxiv.2508.12658

openalex publication_date 2025/08/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We construct new compact manifolds endowed with closed G₂ structures that satisfy the topological properties found by Joyce and Baraglia for the existence of a torsion-free G₂ structure in the same cohomology class. Those manifolds arise as resolutions of orbifolds of the form M/ℤ₂, where M itself does not admit any torsion-free G₂ structure. We develop an equivariant resolution procedure for closed G₂ orbifolds with ℤ₂ isotropy, and analyze some topological properties of the resolved manifolds, including their first Pontryagin class and certain triple Massey products.

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