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This article is cited in 4 scientific papers (total in 4 papers)
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
Abstract:
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.
Key words and phrases:
topological classification, non-degenerate critical point, equipped Reeb graph.
Received: 16.07.2017 Revised: 19.06.2019
Citation:
Bohdana Hladysh, Alexandr Prishlyak, “Simple Morse functions on an oriented surface with boundary”, Zh. Mat. Fiz. Anal. Geom., 15:3 (2019), 354–368
Linking options:
https://www.mathnet.ru/eng/jmag732 https://www.mathnet.ru/eng/jmag/v15/i3/p354
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Abstract page: | 62 | Full-text PDF : | 47 | References: | 16 |
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