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Topology of Functions with Isolated Critical Points on the Boundary of a 2-Dimensional Manifold
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- Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)
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- Symmetry, Integrability and Geometry: Methods and Applications, 2017, том 13
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Topology of Functions with Isolated Critical Points on the Boundary of a 2-Dimensional Manifold
Інший ID:
2010 Mathematics Subject Classification: 57R45; 57R70
DOI:10.3842/SIGMA.2017.050
DOI:10.3842/SIGMA.2017.050
Посилання:
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.
Підтримка:
This paper partially based on the talks of the first author given at the AUI’s seminars on
Topology of functions with isolated critical points on the boundary of a 2-dimensional manifold
(March 2–15, 2017, AUI, Vienna, Austria) and partially supported by the project between the
Austrian Academy of Sciences and the National Academy of Sciences of Ukraine on Modern
Problems in Noncommutative Astroparticle Physics and Categorian Quantum Theory.
Дата:
2017
Переглядів:
461
Завантажень:
258
Анотація:
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.
