Topological equivalence of smooth functions with isolated critical points on a closed surfaces

1999/12/01 by Alexander O. Prishlyak, Alexander Olegovich Prishlyak, Prishlyak, Alexander O.
Mathematics · #57R45 #57R70 #58C27 #Advanced Topology and Set Theory #FOS: Mathematics #Functional Equations Stability Results #Geometric Topology (math.GT) #Mathematical Dynamics and Fractals #math.GT #msc:57R45 #msc:57R70 #msc:58C27

paper · pdf · doi:10.48550/arxiv.math/9912004

12 pages without figures

arxiv created 1999/12/01 · openalex publication_date 1999/12/01 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We consider functions with isolated critical points on a closed surface. We prove that in a neighborhood of a critical point the function conjugates with Rez^k for the some nonnegative integer k. The full topological invariant of such functions is constructed.

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