Classification Problem for Quasitoric Manifolds over a Given Simple Polytope

The classification problem for quasitoric manifolds over a given polytope Pⁿ is considered. The known construction of weights, which was used in the study of the similar problem for toric manifolds, is modified. The construction thus obtained is applied to the solution of the above problem in small dimensions. Classification results are also obtained for polytopes that are products of finitely many simplices of arbitrary dimensions.