Geodesic
Topology of ambient manifolds of non-singular Morse - Smale flows with three periodic orbits
Izvestiya VUZ. Applied Nonlinear Dynamics, Tome 29 (2021) no. 6, pp. 863-868

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The purpose of this study is to establish the topological properties of three-dimensional manifolds which admit Morse - Smale flows without fixed points (non-singular or NMS-flows) and give examples of such manifolds that are not lens spaces. Despite the fact that it is known that any such manifold is a union of circular handles, their topology can be investigated additionally and refined in the case of a small number of orbits. For example, in the case of a flow with two non-twisted (having a tubular neighborhood homeomorphic to a solid torus) orbits, the topology of such manifolds is established exactly: any ambient manifold of an NMS-flow with two orbits is a lens space. Previously, it was believed that all prime manifolds admitting NMS-flows with at most three non-twisted orbits have the same topology. Methods. In this paper, we consider suspensions over Morse - Smale diffeomorphisms with three periodic orbits. These suspensions, in turn, are NMS-flows with three periodic trajectories. Universal coverings of the ambient manifolds of these flows and lens spaces are considered. Results. In this paper, we present a countable set of pairwise distinct simple 3-manifolds admitting NMS-flows with exactly three non-twisted orbits. Conclusion. From the results of this paper it follows that there is a countable set of pairwise distinct three-dimensional manifolds other than lens spaces, which refutes the previously published result that any simple orientable manifold admitting an NMS-flow with at most three orbits is lens space.
Keywords: nonsingular flows, Morse - Smale flows. 
@article{IVP_2021_29_6_a3,
     author = {D. D. Shubin},
     title = {Topology of ambient manifolds of non-singular {Morse} - {Smale} flows with three periodic orbits},
     journal = {Izvestiya VUZ. Applied Nonlinear Dynamics},
     pages = {863--868},
     publisher = {mathdoc},
     volume = {29},
     number = {6},
     year = {2021},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/IVP_2021_29_6_a3/}
}
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D. D. Shubin. Topology of ambient manifolds of non-singular Morse - Smale flows with three periodic orbits. Izvestiya VUZ. Applied Nonlinear Dynamics, Tome 29 (2021) no. 6, pp. 863-868. http://geodesic.mathdoc.fr/item/IVP_2021_29_6_a3/