English

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 G2\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 G2\mathrm{G}_2-structures, the group of automorphisms of a coclosed G2\mathrm{G}_2-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