A new construction of compact torsion-free $G_2$-manifolds by gluing families of Eguchi-Hanson spaces

@article{joyce2017ANC,
  title={A new construction of compact torsion-free \$G\_2\$-manifolds by gluing families of Eguchi-Hanson spaces},
  author={D. joyce and Spiro Karigiannis},
  journal={arXiv: Differential Geometry},
  year={2017}
}
We give a new construction of compact Riemannian 7-manifolds with holonomy $G_2$. Let $M$ be a torsion-free $G_2$-manifold (which can have holonomy a proper subgroup of $G_2$) such that $M$ admits an involution $\iota$ preserving the $G_2$-structure. Then $M/{\langle \iota \rangle}$ is a $G_2$-orbifold, with singular set $L$ an associative submanifold of $M$, where the singularities are locally of the form $\mathbb R^3 \times (\mathbb R^4 / \{\pm 1\})$. We resolve this orbifold by gluing in a… Expand

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