Journal of Mathematical Physics, Analysis, Geometry
2019, vol. 15, No 3, pp. 354-368   https://doi.org/10.15407/mag15.03.354     ( to contents , go back )
https://doi.org/10.15407/mag15.03.354

Simple Morse Functions on an Oriented Surface with Boundary

Bohdana Hladysh

Taras Shevchenko National University of Kyiv, 4-e Akademika Glushkova Ave., Kyiv, 03127, Ukraine
E-mail: biv92@ukr.net

Alexandr Prishlyak

Taras Shevchenko National University of Kyiv, 4-e Akademika Glushkova Ave., Kyiv, 03127, Ukraine
E-mail: prishlyak@yahoo.com

Received July 16, 2017, revised June 19, 2019.

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.

Mathematics Subject Classification 2000: 57R45; 57R70.
Key words: topological classification, non-degenerate critical point, equipped Reeb graph.

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