Basic de Rham cohomology of manifolds with maximal torus action

The family of complex manifolds with maximal torus action introduced by Ishida is a wide family of complex manifolds which includes complex moment-angle and LVMB-manifolds and it is the most general in the sense of admitting certain type of torus action. Any manifold $M$ in this family possesses the canonical foliation $\mathcal{F}$ (like LVMB-manifolds and moment-angle manifolds) which is reconstructed from complex structure and torus action. In the talk, I will present the calculation of basic de Rham cohomology $H_{\mathcal{F}}^*(M)$ obtained in the joined paper with Hiroaki Ishida and Taras Panov. The key ingredients are transverse equivalence of pair $(M, \mathcal{F})$ with a canonical foliation on some moment-angle manifold and the actual calculation for moment-angle manifolds.