| Summary: | <p>We give a new construction of compact Riemannian 7-manifolds with holonomy G2. Let M be a torsion-free G2-manifold (which can have holonomy a proper subgroup of G2) such that M admits an involution ι preserving the G2-structure. Then M/⟨ι⟩ is a G2- orbifold, with singular set L an associative submanifold of M, where the singularities are locally of the form R3×(R4/{±1}). We resolve this orbifold by gluing in a family of Eguchi–Hanson spaces, parametrized by a nonvanishing closed and coclosed 1-form λ on L.</p>
<p>Much of the analytic difficulty lies in constructing appropriate closed G2-structures with sufficiently small torsion to be able to apply the general existence theorem of the first author. In particular, the construction involves solving a family of elliptic equations on the noncompact Eguchi–Hanson space, parametrized by the singular set L. We also present two generalizations of the main theorem, and we discuss several methods of producing examples from this construction.</p>
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