Distinguishing graph of function with three critical points on a closed 3-manifold - Prishlyak, O.; Kiosak, V,; Savchenko, O. (Ukrains’kyi Matematychnyi Zhurnal, 2025)
UDC 515.1 We investigate a critical-point graph as a topological invariant of an isolated critical point of a smooth function on a 3-manifold. The distinguishing graph, which is a complete topological invariant of functions with three critical points on a closed 3-manifold, is constructed. It specifies the partition of a closed 3-manifold into three three-dimensional disks. We prove the criteria of topological equivalence and the realization theorem. The list of all possible distinguishing graphs whose complexity does not exceed 4 is preseted.