Moduli spaces of (co)closed $\mathrm{G}_2$-structures on nilmanifolds
Differential Geometry
2025-03-27 v2
Abstract
We compute the dimensions of some moduli spaces of left-invariant closed and coclosed -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 -structures, the group of automorphisms of a coclosed -structure is not necessarily abelian.
Keywords
Cite
@article{arxiv.2307.04732,
title = {Moduli spaces of (co)closed $\mathrm{G}_2$-structures on nilmanifolds},
author = {Giovanni Bazzoni and Alejandro Gil-García},
journal= {arXiv preprint arXiv:2307.04732},
year = {2025}
}
Comments
17 pages. Sage worksheets available. Journal version