arXiv subjects

Serhii Stas

Publications and source records attributed to Serhii Stas.

2 recordsLinked to original sources

arXiv2023

Structures of the flows with a unique singular point on the 2-dimensional disk

We investigate topological propeties of flows with one singular point and without closed orbits on the 2-dimensional disk. To classify such flows, destingueshed graph is used, which is a two-colored rooted tree imbedded in the plane. We construct a code of the flow and have found all possible structures of the flows with no more then 7 sepapratrices.

math.DS↗

arXiv2023

Topological structure of Morse functions on the projective plane

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).

math.GT↗