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Эта публикация цитируется в 4 научных статьях (всего в 4 статьях)
Simple Morse functions on an oriented surface with boundary
Bohdana Hladysh, Alexandr Prishlyak Taras Shevchenko National University of Kyiv, 4-e Akademika Glushkova Ave., Kyiv, 03127, Ukraine
Аннотация:
In the paper, smooth functions with non-degenerate critical points on a smooth compact surface with boundary are considered. Firstly, it is shown that these functions are topologically equivalent to $m$-functions. The equipped Reeb graph is used to describe their topological structure. Secondly, the authors characterize the topological structure of all simple functions with at most 5 critical points. And finally, a formula for the genus of the surface based on the equipped Reeb graph is obtained.
Ключевые слова и фразы:
topological classification, non-degenerate critical point, equipped Reeb graph.
Поступила в редакцию: 16.07.2017 Исправленный вариант: 19.06.2019
Образец цитирования:
Bohdana Hladysh, Alexandr Prishlyak, “Simple Morse functions on an oriented surface with boundary”, Журн. матем. физ., анал., геом., 15:3 (2019), 354–368
Образцы ссылок на эту страницу:
https://www.mathnet.ru/rus/jmag732 https://www.mathnet.ru/rus/jmag/v15/i3/p354
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Страница аннотации: | 62 | PDF полного текста: | 47 | Список литературы: | 16 |
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