Abstract
We consider m-fields that are generalizations of the Morse–Smale vector fields for manifolds with boundary. We construct complete topological invariants of m-fields on surfaces and m-fields without closed trajectories on three-dimensional manifolds. We also prove criteria for the topological equivalence of m-fields.
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Prishlyak, A.O. Topological Classification of m-Fields on Two- and Three-Dimensional Manifolds with Boundary. Ukrainian Mathematical Journal 55, 966–973 (2003). https://doi.org/10.1023/B:UKMA.0000010596.67853.89
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DOI: https://doi.org/10.1023/B:UKMA.0000010596.67853.89