具有大分次非零对偶斯蒂弗尔-惠特尼类的 Spin 流形
Spin manifolds with nonzero dual Stiefel-Whitney classes of large grading
浏览论文内容
中文总结 AI 辅助
该研究针对 n 维 Spin 流形，探寻使 w̄_j 非零的最大 j 值，得出相关上下界，还补充研究了对应显式流形的构造问题。
中文摘要 AI 辅助
流形 M 的对偶斯蒂弗尔-惠特尼类 w̄_j(M) 是 H^j(M;Z/2) 中的元素，可提供 M 嵌入和浸入欧氏空间的相关信息。我们考虑对每个 n，寻找存在 n 维 Spin 流形且 w̄_j 非零的最大 j 值这一问题，得到了其上界与下界。由于某定理仅证明了此类流形的存在性却未给出显式例子，我们进一步研究寻找 j 尽可能大且 w̄_j 非零的显式流形这一平行问题。
英文摘要
The dual Stiefel-Whitney classes wbar_j(M) of a manifold M are elements of H^j(M;Z/2) which give information about embedding and immersing M in Euclidean space. We consider the question of finding, for each n, the largest j such that there is an n-dimensional Spin manifold with wbar_j nonzero. We obtain upper and lower bounds. Since one theorem proves existence of manifolds without giving explicit examples, we consider a parallel question of finding explicit manifolds with wbar_j nonzero for j as large as possible.
