论文标题
在复杂的射影空间上的亚稳态复杂矢量束
Metastable complex vector bundles over complex projective spaces
论文作者
论文摘要
We apply Weiss calculus to compute the number of topological complex vector bundles of rank $n-2$ with vanishing Chern classes over $\mathbb{C}P^n$ for $n>3$, as given by the list $1, 1, 12, 2, 1, 3, 2, 2, 3, 1, 4, 6, 1, 1, 6, 2, 1, 3, 4, 2, 3, 1, 2, 6$, where the $i$-th此列表中的条目是每当$ n $与$ i $ modulo $ 24 $一致的捆绑包的数量，从$ i = 0 $开始。同样，当$ n> 2 $的排名$ n-1 $捆绑数与$ \ mathbb {c} p^n $超过$ \ mathbb {c} p^n $的数量是$ 2 $时，当$ n $是奇数时，$ n $均匀。
We apply Weiss calculus to compute the number of topological complex vector bundles of rank $n-2$ with vanishing Chern classes over $\mathbb{C}P^n$ for $n>3$, as given by the list $1, 1, 12, 2, 1, 3, 2, 2, 3, 1, 4, 6, 1, 1, 6, 2, 1, 3, 4, 2, 3, 1, 2, 6$, where the $i$-th entry in this list is the number of such bundles whenever $n$ is congruent to $i$ modulo $24$, starting with $i = 0$. Similarly, the number of rank $n-1$ bundles with vanishing Chern classes over $\mathbb{C}P^n$ for $n>2$ is $2$ when $n$ is odd and $1$ when $n$ is even.
