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