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

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.

A compact non-formal closed $G_{2}$ manifold with $b_{1} = 1$

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A compact non-formal closed $G_{2}$ manifold with $b_{1} = 1$

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A compact non-formal closed G2G2​ manifold with b1=1b1​=1

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A compact non-formal closed G2G2​ manifold with b1=1b1​=1

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A compact non-formal closed $G_{2}$ manifold with $b_{1} = 1$

讲解博客

AI智能校验

A compact non-formal closed $G_{2}$ manifold with $b_{1} = 1$

讲解博客

AI智能校验