Deformations in the General Position of the Optimal Functions on Oriented Surfaces with Boundary
Deformations in the General Position of the Optimal Functions on Oriented Surfaces with Boundary
复制标题
有边界定向曲面上最优函数一般位置的变形
DOI：
10.1007/s11253-019-01706-8
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发表时间：
2020
影响因子：
0.5
通讯作者：
O. Prishlyak
中科院分区：
文献类型：
--
作者：
B. Hladysh;O. Prishlyak
我们考虑在具有边界的光滑紧致表面上具有非简并奇点的简单函数。描述了光滑紧致连通面上Morse函数、m函数和mm函数的最优性和极性之间的关系。配备的 Kronrod-Reeb 图的概念用于定义一般位置的变形。此外，我们在环面、有边界的二维圆盘上以及两个环面的连通和上呈现了上述一类的简单函数的变形的完整列表。
We consider simple functions with nondegenerate singularities on smooth compact oriented surfaces with boundary. The relationship between the optimality and polarity of Morse functions,m-functions andmm-functions on smooth compact oriented connected surfaces is described. The concept of equipped Kronrod–Reeb graph is used to define deformation in the general position. Moreover, we present the entire list of deformations of simple functions of one of the classes described above on a torus, on a 2-dimensional disk with boundary, and on the connected sum of two tori.