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Abstract
To each isolated critical point of a smooth function on a 3-manifold we put in correspondence a tree (graph without cycles). We will prove that functions are topologically equivalent in the neighbourhoods of critical points if and only if the corresponding trees are isomorphic. A complete topological invariant of functions with fore critical points, on a closed 3-manifold, was constructed. A criterion for the topological equivalence of functions with a finite number of critical points on 3-manifolds is given.
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