Topological structure of Morse functions on the projective plane

Svitlana Bilun; Alexandr Prishlyak; Serhii Stas; Alina Vlasenko

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arXiv · 2303.03850

Topological structure of Morse functions on the projective plane

Svitlana Bilun·Alexandr Prishlyak·Serhii Stas·Alina Vlasenko

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Abstract

To investigate the topological structure of Morse functions on the projective plane we use the Reeb graphs. We describe it properties and prove that it is a complete topological invariant of simple Morse function on $\mathbb{R} P^2$. We prove recurent formulas for the number of Reeb graphs with the given number of sadles (vertex).

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Svitlana Bilun, Alexandr Prishlyak, Serhii Stas, Alina Vlasenko. 2023-03-07. Topological structure of Morse functions on the projective plane. https://arxiv.org/abs/2303.03850

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