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arXiv · 2510.25511

Purely coclosed $\mathrm{G}_2$-structures on nilmanifolds -- II

Giovanni Bazzoni·Giorgia Petracci
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Abstract

This paper completes the classification of seven-dimensional nilpotent Lie groups endowed with a left-invariant purely coclosed $\text{G}_2$-structure, initiated by the first-named author and collaborators. In this previous work, the authors provided the classification of decomposable seven-dimensional nilpotent Lie groups and of the indecomposable ones up to step $4$ of nilpotency. Here, we address the case of indecomposable $5$- and $6$-step nilpotent Lie groups.

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Giovanni Bazzoni, Giorgia Petracci. 2025-10-29. Purely coclosed $\mathrm{G}_2$-structures on nilmanifolds -- II. https://arxiv.org/abs/2510.25511

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