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

B. I. Hladysh; A. O. Prishlyak

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arXiv · 1905.09072

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

B. I. Hladysh·A. O. Prishlyak

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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 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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BibTeX RIS

B. I. Hladysh, A. O. Prishlyak. 2019-05-22. Topological structure of functions with isolated critical points on a 3-manifold. https://arxiv.org/abs/1905.09072

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