Characterization of locally standard, Z-equivariantly formal manifolds in general position

We give a characterization of locally standard, Z-equivariantly formal manifolds in general position. In particular, we show that for dimension 2n at least 10, to every such manifold with labeled GKM graph there is an equivariantly formal torus manifold such that the restriction of the Tⁿ-action to a certain T^n-1-action yields the same labeled graph, thus showing that the (equivariant) cohomology with Z-coefficients of those manifolds has the same description as that of equivariantly formal torus manifolds.