Multiple points of immersions of M6 ↬ (ℝ7)

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 characteristic numbers of these manifolds. By a certain method, these numbers can be read of from the Hurewicz image of h:π7QMO(1)→H7QMO(1)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.