A combinatorial invariant of gradient-like flows on a connected sum of $\mathbb{S}^{n-1}\times\mathbb{S}^1$

We obtain necessary and sufficient conditions for the topological equivalence of gradient-like flows without heteroclinic intersections defined on the connected sum of a finite number of manifolds homeomorphic to $\mathbb{S}^{n-1}\times \mathbb{S}^1$, $n\geq 3$. For $n>3$, this result extends substantially the class of manifolds such that structurally stable systems on these manifolds admit a topological classification. Bibliography: 36 titles.