On the Euler Characteristic of Multiple Selfintersection Points of Immersed Manifolds

Various examples of immersed codimension 1 manifolds are studied from the viewpoint of possible combinations of the Euler characteristics of the submanifolds of multiple selfintersection points. A complete answer is given for the immersed 5-manifolds in the 6-dimensional Euclidean space. Relations are discussed with other constructions in differential topology and singularity theory.