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

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.

17 pages. Sage worksheets available. Journal version

References in corpus (4)

• New invariants of G_2-structures
• Nilmanifolds with a calibrated G_2-structure
• On the automorphism group of a closed G${}_2$-structure
• Purely coclosed G${}_2$-structures on 2-step nilpotent Lie groups