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In the present paper we consider class $G$ of orientation preservingMorse-Smale diffeomorphisms $f$, which defined on closed 3-manifold $M^3$, andwhose non-wandering set consist of four fixed points with pairwise differentMorse indices. It follows from S. Smale and K. Meyer results that allgradient-like flows with similar properties has Morse energy function with fourcritical points of pairwise different Morse indices. This implies, thatsupporting manifold $M^3$ for these flows admits a Heegaard decomposition ofgenus 1 and hence it is homeomorphic to a lens space $L_{p,q}$. Despite thesimple structure of the non-wandering set in class $G$ there existdiffeomorphisms with wild embedded separatrices. According to V. Grines, F.Laudenbach, O. Pochinka results such diffeomorphisms do not possesses an energyfunction, and question about topology their supporting manifold is open.According to V. Grines, E. Zhuzhoma and V. Medvedev results $M^3$ ishomeomorphic to a lens space $L_{p,q}$ in case of tame embedding of closures ofone-dimensional separatrices of diffeomorphism $f\in G$. Moreover, thewandering set of $f$ contains at least $p$ non-compact heteroclinic curves. Inthe present paper similar result was received for arbitrary diffeomorphisms ofclass $G$. Also we construct diffeomorphisms from $G$ with wild embeddingone-dimensional separatrices on every lens space $L_{p,q}$. Such examples wereknown previously only on the 3-sphere.

On the topology of 3-manifolds admitting Morse-Smale diffeomorphisms with four fixed points of pairwise different Morse indices