Svitlana Bilun, Bohdana Hladysh, Alexandr Prishlyak, Mariia Roman
Published 2023-04-10Version 1
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.
Comments: 9 pages, 4 figures
Examples of smooth maps with finitely many critical points in dimensions $(4,3)$, $(8,5)$ and $(16,9)$
Manifolds which admit maps with finitely many critical points into spheres of small dimensions
On smooth maps with finitely many critical points
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