# 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}
}
• Published 2017
• Mathematics
• arXiv: Differential Geometry
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
28 Citations

#### References

SHOWING 1-10 OF 54 REFERENCES
K3 surfaces with non-symplectic involution and compact irreducible G2-manifolds
• Mathematics
• Mathematical Proceedings of the Cambridge Philosophical Society
• 2011