G₂-manifolds and coassociative torus fibration

Abstract

Let (φ₀, g₀) be a flat G₂-structure on the torus T⁷. For a certain finite group Γ-action on T⁷ preserving the G₂-structure, Joyce constructed a closed G₂-manifold M from the resolution of the orbifold T⁷/Γ. The main purpose of this paper is to prove that there exist global coassociative fibrations on open submanifolds of certain Joyce manifolds.

Keywords

G2-manifold / coassociative torus fibration / Gromov-Hausdorff convergence

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