arXiv subjects

Bohdana Hladysh

Publications and source records attributed to Bohdana Hladysh.

2 recordsLinked to original sources

arXiv2023

Morse functions with four critical points on immersed 2-spheres

We investigate topological properties of simple Morse functions with 4 critical points on immersed 2-spheres. To classify such functions, dual graph of immersion and Reeb graphs is used. We have found all possible structures of the functions:6 structures with 4 critical points on one 1-strata component, 7 structures with two points on the 1-strata and two points on the 2-strata, 7 structures with two 1-stratas and a three-connected 2-strata, three structures with two 1-stratas and without a three-connected 2-strata.

math.GT↗

arXiv2023

Gradient vector fields of codimension one on the 2-sphere with at most ten singular points

We describe all possible topological structures of codimension one gradient vector fields on the shpere with at most ten singular points. To describe structures, we use a graph whose edges are one-dimensional stable manifolds. The saddle-node singularity is specified by selecting a pair of vertices-edge or edge-face, and the saddle connection is specified by a T-vertex.

math.DS↗