Distinguishing graph of function with three critical points on a closed 3-manifold
UDC 515.1 We investigate a critical-point graph as a topological invariant of an isolated critical point of a smooth function on a 3-manifold. The distinguishing graph, which is a complete topological invariant of functions with three critical points on a closed 3-manifold, is construct...
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| Datum: | 2025 |
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| Hauptverfasser: | , , , , , , |
| Format: | Artikel |
| Sprache: | Ukrainisch |
| Veröffentlicht: |
Institute of Mathematics, NAS of Ukraine
2025
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| Online Zugang: | https://umj.imath.kiev.ua/index.php/umj/article/view/8095 |
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| Назва журналу: | Ukrains’kyi Matematychnyi Zhurnal |
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Ukrains’kyi Matematychnyi Zhurnal| Zusammenfassung: | UDC 515.1
We investigate a critical-point graph as a topological invariant of an isolated critical point of a smooth function on a 3-manifold. The distinguishing graph, which is a complete topological invariant of functions with three critical points on a closed 3-manifold, is constructed. It specifies the partition of a closed 3-manifold into three three-dimensional disks. We prove the criteria of topological equivalence and the realization theorem. The list of all possible distinguishing graphs whose complexity does not exceed 4 is preseted. |
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| DOI: | 10.3842/umzh.v77i1.8095 |