Morse functions with four critical points on immersed 2-spheres

Svitlana Bilun; Bohdana Hladysh; Alexandr Prishlyak; Mariia Roman

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arXiv · 2304.04392

Morse functions with four critical points on immersed 2-spheres

Svitlana Bilun·Bohdana Hladysh·Alexandr Prishlyak·Mariia Roman

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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.

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Svitlana Bilun, Bohdana Hladysh, Alexandr Prishlyak, Mariia Roman. 2023-04-10. Morse functions with four critical points on immersed 2-spheres. https://arxiv.org/abs/2304.04392

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