The problem of discriminating algorithmically the standard three-dimensional sphere

A constructive topological invariant, uniquely determining the Heegaard diagrams of the standard sphere in the class of all Heegaard diagrams of three-dimensional manifolds, is formed. The sufficiency of this invariant is proved by the methods of Morse theory. That this invariant is trivial in the class of Heegaard diagrams for the standard sphere is proved for certain infinite sequences, and on the remaining diagrams for the standard sphere the presence of the invariant is corroborated by a trial calculation on the electronic computer BESM-6, in which representations of the standard sphere were examined.