论文标题
在理性的同位偏度指数上
On the rational homotopical nilpotency index of principal bundles
论文作者
论文摘要
令$ \ rm {aut}（p）$表示主$ g $ -bundle $ p：e \ rightarrow x $简单地连接的CW Complextes的所有自纤维同质等价的空间，都使用$ e $有限。当$ g $是一个紧凑的连接拓扑组时，我们表明存在不平等$ n - {\ rm n}（p）\ leq {\ rm hnil} _ {\ m athbb {q}}}}}}}（\ rm {aut}}（aut}}（p）（p）（p）_0 _0 $ n $第2节中定义了$ g $和$ g $和$ {\ rm n}（p）$的非平凡的有理同质组。有限。
Let $\rm{Aut}(p)$ denote the space of all self-fibre homotopy equivalences of a principal $G$-bundle $p: E\rightarrow X$ of simply connected CW complexes with $E$ finite. When $G$ is a compact connected topological group, we show that there exists an inequality $$n-{\rm N}(p)\leq {\rm Hnil}_{\mathbb{Q}}({\rm{Aut}}(p)_0)\leq n$$ for any space $X$, where $n$ is the number of non-trivial rational homotopy groups of $G$ and ${\rm N}(p)$ is defined in Section 2. In particular, ${\rm Hnil}_{\mathbb{Q}}({\rm{Aut}}(p)_{0})=n$ if $p$ is a fibre-homotopy trivial bundle and X is finite.
