Dolbeault formality of Bogomolov–Guan manifolds

Determine whether Bogomolov–Guan manifolds are Dolbeault formal and, if they are not, construct explicit Dolbeault, Bott–Chern, or Aeppli Massey-type operations detecting their nonformality.

Background

The paper proves de Rham nonformality for all Bogomolov–Guan manifolds of complex dimension at least four, but explicitly distinguishes this result from the unresolved question of Dolbeault formality. Dolbeault formality concerns the complex-homotopical structure and is not settled by the de Rham obstruction.

The proposed direction is to investigate whether the invariant complex geometry of the Bogomolov–Guan precursor supports suitable complex-homotopical obstructions, and whether such obstructions can be transferred through the finite quotient and the subsequent resolution.