Remarks on the classification of quasitoric manifolds up to equivariant   homeomorphism
  We give three sufficient criteria for two quasitoric manifolds (M,M') to be (weakly) equivariantly homeomorphic.   We apply these criteria to count the weakly equivariant homeomorphism types of quasitoric manifolds with a given cohomology ring. 
Michael Wiemeler
math.GT math.AT