Topological classification of flows without heteroclinic intersections on a connected sum of manifolds $\mathbb{S}^{n-1}\times\mathbb{S}^{1}$

In this paper, we announce a result on the possibility of obtaining sufficient conditions for topological conjugacy of gradient-like flows without heteroclinic intersections, given on a connected sum of products $S^{n-1}\times S^1$ in combinatorial terms.