Topology of Ambient 3-Manifolds of Non-Singular Flows with Twisted Saddle Orbit
Received 26 December 2022; accepted 25 August 2023; published 28 September 2023
2023, Vol. 19, no. 3, pp. 371-381
Author(s): Pochinka O. V., Shubin D. D.
In the present paper, nonsingular Morse – Smale flows on closed orientable 3-manifolds are
considered under the assumption that among the periodic orbits of the flow there is only one
saddle and that it is twisted. An exhaustive description of the topology of such manifolds is
obtained. Namely, it is established that any manifold admitting such flows is either a lens space
or a connected sum of a lens space with a projective space, or Seifert manifolds with a base
homeomorphic to a sphere and three singular fibers. Since the latter are prime manifolds, the
result obtained refutes the claim that, among prime manifolds, the flows considered admit only
lens spaces.
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