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Regular version of the site

Article

On Topology of Manifolds Admitting a Gradient-Like Flow with a Prescribed Non-Wandering Set

Siberian Advances in Mathematics. 2019. Vol. 29. No. 2. P. 116-127.

We study relations between the structure of the set of equilibrium points of a gradient-like flows

and the topology of the support manifold of dimension 4 and higher. We introduce a class

of manifolds that admit a generalized Heegaard splitting. We consider gradient-like 

flows such that the non-wandering set consists of exactly μ node and ν

saddle equilibrium points of indices equal to either 1 or n − 1. We show that, for such a 

flow, there exists a generalized Heegaard splitting of the support manifold of genius

g =( ν − μ+2)/2. We also suggest an algorithm for constructing gradient-like flows on closed manifolds of dimension 3

and higher with prescribed numbers of node and saddle equilibrium points of prescribed indices.