关键词: Immersion, Hurewicz homomorphism, spherical classes, Stiefel-Whitney number

Abstract:

In this article, we determine the multiple point set of immersions of 6-dimensional manifolds into 7-dimensional Euclidean space R7. The method is to evaluate the charac-teristic numbers of these manifolds. By a certain method, these numbers can be read of from the Hurewicz image of

h : π₇QMO(1) →H₇QMO(1).
In particular, we show that for any immersion of P⁶ in R⁷ the double, 4-fold and 6-fold point manifolds are cobordant to boundaries and triple point manifolds cobordant to P⁴, 5-fold point manifolds cobordant to P² and 7-fold point manifold are odd number.

Key words: Immersion, Hurewicz homomorphism, spherical classes, Stiefel-Whitney number