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arXiv · 2005.04924

A compact non-formal closed $G_2$ manifold with $b_1=1$

Lucía Martín-Merchán
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Abstract

We construct a compact manifold with a closed $G_2$ structure not admitting any torsion-free $G_2$ structure, which is non-formal and has first Betti number $b_1=1$. We develop a method of resolution for orbifolds that arise as a quotient $M/Z_2$ with $M$ a closed $G_2$ manifold under the assumption that the singular locus carries a nowhere-vanishing closed 1-form.

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Lucía Martín-Merchán. 2020-05-11. A compact non-formal closed $G_2$ manifold with $b_1=1$. https://arxiv.org/abs/2005.04924

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