7 papers
Topological classification of Morse-Smale flows on 3-manifolds
Alexandr Prishlyak
We construct a topological invariant for a Morse-Smale flow on a 3-manifold and prove that the flows are topologically equivalent iff their invariants are same.
Topological equivalence of smooth functions with isolated critical points on a closed surfaces
Alexander O. Prishlyak
We consider functions with isolated critical points on a closed surface. We prove that in a neighborhood of a critical point the function conjugates with Re for the some nonne…
Gradient like Morse-Smale dynamical systems on 4-manifolds
Alexander O. Prishlyak
The complete invariant for gradient like Morse-Smale dynamical systems (vector fields and diffeomorphisms) on closed 4-manifolds are constructed. It is same as Kirby diagram in a c…
Vector fields with a given set of singular points
A. O. Prishlyak
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 b…
Minimal handle decomposition of smooth simply connected 5-manifolds
A. O. Prishlyak
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…
Conjugation of Morse Function on 3-Manifolds
Alexander Prishlyak
The questions when two Morse function on closed manifolds are conjugated is investigated. Using the handle decompositions of manifolds the condition of conjugation is formulated. F…