Geodesic
Simple Morse functions on an oriented surface with boundary
Žurnal matematičeskoj fiziki, analiza, geometrii, Tome 15 (2019) no. 3, pp. 354-368 Cet article a éte moissonné depuis la source Math-Net.Ru

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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. 
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Bohdana Hladysh; Alexandr Prishlyak. Simple Morse functions on an oriented surface with boundary. Žurnal matematičeskoj fiziki, analiza, geometrii, Tome 15 (2019) no. 3, pp. 354-368. http://geodesic.mathdoc.fr/item/JMAG_2019_15_3_a3/

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