Quaternionic Bott-Chern Cohomology and existence of HKT metrics

We study quaternionic Bott-Chern cohomology on compact hypercomplex manifolds and adapt some results from complex geometry to the quaternionic setting. For instance, we prove a criterion for the existence of hyperkahler with torsion metrics on compact hypercomplex manifolds of real dimension 8 analogous to the one given by Teleman [34] and Angella et al. [3] for compact complex surfaces.