Topological Classification of <em class="a-plus-plus">m</em>-Fields on Two- and Three-Dimensional Manifolds with Boundary

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.