Topological structure of Morse functions on the projective plane

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).

arXiv comment8 pages, 4 figures