Bott-Chern cohomology
= Bott-Chern cohomology
{c}
{title2=$H_{BC}^{p,q}(M)$}
For a <complex manifold>, Bott-Chern cohomology is
$$
H_{BC}^{p,q}(M)=\frac{\ker\partial\cap\ker\bar\partial\subseteq\mathcal A^{p,q}(M)}{\partial\bar\partial\mathcal A^{p-1,q-1}(M)}.
$$
Its classes are represented by $d$-closed forms of pure type. A natural map sends a Bott-Chern class to its <Dolbeault cohomology> class.