Topology of Functions with Isolated Critical Points on the Boundary of a 2-Dimensional Manifold

Symmetry Integrability and Geometry-Methods and Applications

article

Bohdana I. Hladysh¹  Aleksandr O. Prishlyak¹ 

[1] Faculty of Mechanics and Mathematics, Taras Shevchenko National University of Kyiv

关键词: topological classification;    isolated boundary critical point;    optimal function;    chord diagram;   

DOI  :  10.3842/SIGMA.2017.050

来源: National Academy of Science of Ukraine

【 摘 要 】

This paper focuses on the problem of topological equivalence of functions with isolated critical points on the boundary of a compact surface $M$ which are also isolated critical points of their restrictions to the boundary. This class of functions we denote by $\Omega(M)$. Firstly, we've obtained the topological classification of above-mentioned functions in some neighborhood of their critical points. Secondly, we've constructed a chord diagram from the neighborhood of a critical level. Also the minimum number of critical points of such functions is being considered. And finally, the criterion of global topological equivalence of functions which belong to $\Omega(M)$ and have three critical points has been developed.

【 授权许可】

Unknown