Topological structure of functions with isolated critical points on a 3-manifold
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 topologica...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
| Published: |
Odesa National University of Technology
2023-11-01
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| Series: | Pracì Mìžnarodnogo Geometričnogo Centru |
| Subjects: | |
| Online Access: | https://journals.ontu.edu.ua/index.php/geometry/article/view/2512 |
| Summary: | 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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| ISSN: | 2072-9812 2409-8906 |