Complex moment-angle manifolds are equivariantly rigid, so their equivariant homotopy type determines their equivariant homeomorphism type, with similar but partial results for quaternionic moment-angle manifolds.
Available at https://pi.math.cornell.edu/˜hatcher/VBKT/VBpage.html
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Topological rigidity of complex and quaternionic moment--angle manifolds
Complex moment-angle manifolds are equivariantly rigid, so their equivariant homotopy type determines their equivariant homeomorphism type, with similar but partial results for quaternionic moment-angle manifolds.