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

Lucía Martín-Merchán

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

Differential Geometry 2021-02-15 v2

Authors: Lucía Martín-Merchán

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.

Keywords

closed G2 manifold non-formal manifold betti number orbifold resolution closed 1-form

Cite

@article{arxiv.2005.04924,
  title  = {A compact non-formal closed $G_2$ manifold with $b_1=1$},
  author = {Lucía Martín-Merchán},
  journal= {arXiv preprint arXiv:2005.04924},
  year   = {2021}
}

Comments

31 pages. v2 corrects a mistake on the definition of \hat{\omega}_1. To appear in Math Nach

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