Realization of Fomenko-Zieschang invariants in closed symplectic manifolds with contact singularities

The topological bifurcations of Liouville foliations on invariant -manifolds that are induced by attaching toric -handles are investigated. It is shown that each marked molecule (Fomenko-Zieschang invariant) can be realized on an invariant submanifold of a closed symplectic manifold with contact singularities which is obtained by attaching toric -handles sequentially to a set of symplectic manifolds, while these latter have the structures of locally trivial fibrations over associated with atoms. Bibliography: 10 titles.