Comparison conjecture for complex and almost complex threefold moduli

Let $\mathcal Z(\operatorname{Cpx}_3)$ denote the moduli space or parameter space of complex threefolds used in the paper, and let $\mathcal Z(\operatorname{ACpx}_3)$ denote its almost complex analogue. Their compactly supported cohomology groups are related by the natural map

$$H^*_c(\mathcal Z(\operatorname{Cpx}_3))\longrightarrow H^*_c(\mathcal Z(\operatorname{ACpx}_3)).$$

Complex–almost complex comparison conjecture. This map is an isomorphism. The conjecture is intended to permit almost complex methods to study invariants of complex threefolds, but no resolution is supplied in the source.