Topology of Functions with Isolated Critical Points on the Boundary of a 2-Dimensional Manifold

• Published in: Symmetry, Integrability and Geometry: Methods and Applications
• Date: 2017
• Main Authors: Hladysh, B.I., Prishlyak, A.O.
• Format: Article
• Language: English
• Published: Інститут математики НАН України 2017
• Online Access: https://nasplib.isofts.kiev.ua/handle/123456789/148582
• Journal Title: Digital Library of Periodicals of National Academy of Sciences of Ukraine
• Cite this: Topology of Functions with Isolated Critical Points on the Boundary of a 2-Dimensional Manifold / B.I. Hladysh, A.O. Prishlyak // Symmetry, Integrability and Geometry: Methods and Applications. — 2017. — Т. 13. — Бібліогр.: 19 назв. — англ.

This paper focuses on the problem of topological equivalence of functions with isolated critical points on the boundary of a compact surface M which are also isolated critical points of their restrictions to the boundary. This class of functions we denote by Ω(M). Firstly, we've obtained the topological classification of above-mentioned functions in some neighborhood of their critical points. Secondly, we've constructed a chord diagram from the neighborhood of a critical level. Also the minimum number of critical points of such functions is being considered. And finally, the criterion of global topological equivalence of functions which belong to Ω(M) and have three critical points has been developed.