Morse functions with four critical points on immersed 2-spheres
Geometric Topology
2023-04-11 v1
Abstract
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.
Keywords
Cite
@article{arxiv.2304.04392,
title = {Morse functions with four critical points on immersed 2-spheres},
author = {Svitlana Bilun and Bohdana Hladysh and Alexandr Prishlyak and Mariia Roman},
journal= {arXiv preprint arXiv:2304.04392},
year = {2023}
}
Comments
9 pages, 4 figures