环Stiefel流形的同伦分解及其指数
Homotopy Decompositions of Looped Stiefel manifolds, and their Exponents
摘要：
设$p$是奇素数，并固定整数$m$和$n$，使得$0<m<n\leq (p-1)(p-2)$。给出了复Stiefel流形$W_{n,m}$的闭路空间的$p$ -局部同伦分解.给出了实Stiefel流形和辛Stiefel流形的闭路空间的类似分解。作为这些分解的一个应用，我们计算了$W_{n,m}$的$p$ -指数的上界。还计算了稳定范围$2m<n$和$0<m\leq (p-1)(p-2)$中$p$ -指数的上界。
英文摘要：
Let $p$ be an odd prime, and fix integers $m$ and $n$ such that $0<m<n\leq (p-1)(p-2)$. We give a $p$-local homotopy decomposition for the loop space of the complex Stiefel manifold $W_{n,m}$. Similar decompositions are given for the loop space of the real and symplectic Stiefel manifolds. As an application of these decompositions, we compute upper bounds for the $p$-exponent of $W_{n,m}$. Upper bounds for $p$-exponents in the stable range $2m<n$ and $0<m\leq (p-1)(p-2)$ are computed as well.
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