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Symmetry, Integrability and Geometry: Methods and Applications, 2017, Volume 13, 050, 17 pp.
DOI: https://doi.org/10.3842/SIGMA.2017.050
(Mi sigma1250)
 

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
Full-text PDF (456 kB) Citations (9)
References:
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.
Funding agency Grant number
National Academy of Sciences of Ukraine
Austrian Science Fund
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.
Received: November 18, 2016; in final form June 16, 2017; Published online July 1, 2017
Bibliographic databases:
Document Type: Article
MSC: 57R45; 57R70
Language: English
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.
Citation in format AMSBIB
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\paper Topology of Functions with Isolated Critical Points on the Boundary of~a~2-Dimensional Manifold
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\vol 13
\papernumber 050
\totalpages 17
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  • This publication is cited in the following 9 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    Symmetry, Integrability and Geometry: Methods and Applications
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