Prem-mappings,triple self-intersection points of oriented surfaces,and the Rokhlin signature theorem

We find a connection between the Rokhlin theorem on the signature of a four-dimensional manifold and the notion of a prem-mapping that arises from the theory of embeddings of smooth manifolds. Translated fromMatematicheskie Zametki, Vol. 59, No. 6, pp. 803–810, June, 1996. I thank Prof. A. Szucs for informing me about the existence of a canonical orientationO on the double points curve of a prem-mapping of an oriented surface into ℝ³.