On the Euler characteristic of multiple selfintersection points of immersed manifolds

P. M. Akhmet'ev^a, I. Maleshich^b, D. Repovš<sup>b

a</sup> Institute of Terrestrial Magnetism, Ionosphere and Radio Wave Propagation
^b University of Ljubljana

Abstract: 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.

Keywords: immersion, Euler characteristic, singularity, selfintersection.

UDC: 515.142

Received: 20.09.2002

 English version: Siberian Mathematical Journal, 2003, 44:2, 208–212

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