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arXiv · 2307.04732

Moduli spaces of (co)closed $\mathrm{G}_2$-structures on nilmanifolds

Giovanni Bazzoni·Alejandro Gil-García
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Abstract

We compute the dimensions of some moduli spaces of left-invariant closed and coclosed $\mathrm{G}_2$-structures on 7-dimensional nilmanifolds, showing that they are not related to the third Betti number. We also prove that, in contrast to the case of closed $\mathrm{G}_2$-structures, the group of automorphisms of a coclosed $\mathrm{G}_2$-structure is not necessarily abelian.

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Giovanni Bazzoni, Alejandro Gil-García. 2023-07-10. Moduli spaces of (co)closed $\mathrm{G}_2$-structures on nilmanifolds. https://doi.org/10.1093/qmath/haae037

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