Bott-Chern and $\bar{\partial }$ Harmonic forms on Almost Hermitian 4-manifolds

Tom Holt

We prove that on a compact almost Hermitian 4-manifold the space of $\bar{\partial }$-harmonic $(1,1)$-forms always has dimension $h_{\bar{\partial }}^{1,1}=b_{-}+1$ or $b_{-}$, whilst th…