The basic Dolbeault cohomology of the canonical foliation on complex moment-angle manifolds and manifolds with maximal torus action admits a Hodge decomposition and is generated by degree (1,1) classes.
Derived subdivisions make every PL sphere polytopal
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Dolbeault cohomology of complex manifolds with torus action
The basic Dolbeault cohomology of the canonical foliation on complex moment-angle manifolds and manifolds with maximal torus action admits a Hodge decomposition and is generated by degree (1,1) classes.