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

The topological bifurcations of Liouville foliations on invariant $3$-manifolds that are induced by attaching toric $\Theta$-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 $\Theta$-handles sequentially to a set of symplectic manifolds, while these latter have the structures of locally trivial fibrations over $S^1$ associated with atoms.
Bibliography: 10 titles.