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This article is cited in 9 scientific papers (total in 9 papers)
Topology of Functions with Isolated Critical Points on the Boundary of a 2-Dimensional Manifold
Bohdana I. Hladysh, Aleksandr O. Prishlyak Faculty of Mechanics and Mathematics, Taras Shevchenko National University of Kyiv, 4-e Akademika Glushkova Ave., Kyiv, 03127, Ukraine
Abstract:
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 $\Omega(M)$. 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 $\Omega(M)$ and have three critical points has been developed.
Keywords:
topological classification; isolated boundary critical point; optimal function; chord diagram.
Received: November 18, 2016; in final form June 16, 2017; Published online July 1, 2017
Citation:
Bohdana I. Hladysh, Aleksandr O. Prishlyak, “Topology of Functions with Isolated Critical Points on the Boundary of a 2-Dimensional Manifold”, SIGMA, 13 (2017), 050, 17 pp.
Linking options:
https://www.mathnet.ru/eng/sigma1250 https://www.mathnet.ru/eng/sigma/v13/p50
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Abstract page: | 150 | Full-text PDF : | 38 | References: | 29 |
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