摘要
Let n≥4 and let M^n be a smooth closed n-manifold. Denote the number of the powersin the binary expression of n by α(n). In this paper, we determine, up to cobordism, allthe possible M^n which immerse themselves in R^(2n-α(n)-1), and prove that the Stiefel-Whitneynumber W_(n-α(n))W_α(n) (M^n)=0 iff M^n is cobordant to a smooth closed n-manifold N^n, whereN^n immerses itself in R^(2n-α(n)-1).
Let n≥4 and let M<sup>n</sup> be a smooth closed n-manifold. Denote the number of the powersin the binary expression of n by α（n）. In this paper, we determine, up to cobordism, allthe possible M<sup>n</sup> which immerse themselves in R<sup>2n-α（n）-1</sup>, and prove that the Stiefel-Whitneynumber W<sub>n-α（n）</sub>W<sub>α</sub>（n） （M<sup>n</sup>）=0 iff M<sup>n</sup> is cobordant to a smooth closed n-manifold N<sup>n</sup>, whereN<sup>n</sup> immerses itself in R<sup>2n-α（n）-1</sup>.
基金
Project supported by the National Natural Science Foundation of China.
