A remark on elimination of singularities for mappings of 4-manifolds into 3-manifolds

It is known that the homological obstruction to the existence of a fold mapping from an orientable closed 4-manifold into R3 vanishes. Nevertheless some 4-manifolds do not admit a fold mapping into R3. For example, O. Saeki proved that there is no fold mapping of the standard complex projective plane CP2 into R3. In the paper we give an elementary proof of this fact.