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Classification of NMS-flows with unique twisted saddle orbit on orientable 4-manifolds
Topological equivalence of Morse-Smale flows without fixed points
(NMS-flows) under assumptions of different generalities was studied in
a number of papers. In some cases when the number of periodic orbits
is small, it is possible to give exhaustive classification, namely to provide
the list of all manifolds that admit flows of considered class, find complete
invariant for topological equivalence and introduce each equivalence class
with some representative flow. This work continues the series of such
articles. We consider the class of NMS-flows with unique saddle orbit,
under the assumption that it is twisted, on closed orientable 4-manifolds
and prove that the only 4-manifold admitting the considered flows is the
manifold S3 × S1. Also, it is established that such flows are split into
exactly eight equivalence classes and construction of a representative for
each equivalence class is provided