arXiv subjects
Publications and source records attributed to A. O. Prishlyak.
To each isolated critical point of a smooth function on a 3-manifold we put in correspondence a tree (graph without cycles). We will prove that functions are topologically equivalent in the neighborhoods of critical points if and only if the corresponding trees are isomorphic. A complete topological invariant of functions with isolated critical points, on a closed 3-manifold, will be constructed.
A theorem on the existence of the unique minimal topologic handle decomposition of differentiable simply connected five-dimensional manifolds is proved. For a decomposition of this sort, the number of handles of each index is given.
Theorems on the existence of vector fields with given sets of Indexes of isolated Singular points are proved for the cases of closed manifolds, pairs of manifolds, manifolds with boundary, and gradient fields. It is proved that, on a two-dimensional manifold, an index of an isolated Singular point of the gradient field is not greater than one.
The topological classification of gradient like Morse-Smale vector fields and diffeomorphisms on 3-manifolds was obtained.