Topological structure of functions with isolated critical points on a 3-manifold

2019/05/22 by Bohdana Hladysh, Hladysh, B. I., Alexandr Prishlyak +1
Computer Science · Mathematics · #57R45 #57R70 #58C27 #FOS: Mathematics #Geometric Topology (math.GT) #Mathematical Dynamics and Fractals #Topological and Geometric Data Analysis #advanced mathematical theories

paper · pdf · doi:10.48550/arxiv.1905.09072

openalex publication_date 2019/05/22 · openalex created_date 2023/11/13 · openalex updated_date 2026/07/28

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 neighborhoods of critical points if and only if the corresponding trees are isomorphic. A complete topological invariant of functions with isolated critical points, on a closed 3-manifold, will be constructed.

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